keyword:new - cp's OEIS frontend

A387110 Number of ways to choose a sequence of distinct integer partitions, one of each prime index of n.

1, 1, 2, 0, 3, 2, 5, 0, 2, 3, 7, 0, 11, 5, 6, 0, 15, 2, 22, 0, 10, 7, 30, 0, 6, 11, 0, 0, 42, 6, 56, 0, 14, 15, 15, 0, 77, 22, 22, 0, 101, 10, 135, 0, 6, 30, 176, 0, 20, 6, 30, 0, 231, 0, 21, 0, 44, 42, 297, 0, 385, 56, 10, 0, 33, 14, 490, 0, 60, 15, 627, 0

Offset: 1

Gus Wiseman, Aug 18 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The axiom of choice says that, given any sequence of nonempty sets, it is possible to choose a sequence containing an element from each. In the strict version, the elements of this sequence must be distinct, meaning none is chosen more than once.

			The prime indices of 9 are (2,2), and there are a(9) = 2 choices:
  ((2),(1,1))
  ((1,1),(2))
The prime indices of 15 are (2,3), and there are a(15) = 5 choices:
  ((2),(3))
  ((2),(2,1))
  ((2),(1,1,1))
  ((1,1),(2,1))
  ((1,1),(1,1,1))

Positions of zeros are A276078 (choosable), complement A276079 (non-choosable).
Allowing repeated partitions gives A299200, A357977, A357982, A357978.
For multiset systems see A355529, A355744, A367771, set systems A367901-A367905.
For divisors see A355731, A355733, A355734, A355735, A355737, A355739, A355740.
For prime factors instead of partitions see A355741, A355742, A387136.
The disjoint case is A383706.
For initial intervals instead of partitions we have A387111.
The case of strict partitions is A387115.
The case of constant partitions is A387120.
Taking each prime factor (instead of index) gives A387133.
A000041 counts integer partitions, strict A000009.
A003963 multiplies together prime indices.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A008284, A063834, A261049, A296122, A299201, A335433, A335448, A355745, A387135.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Tuples[IntegerPartitions/@prix[n]],UnsameQ@@#&]],{n,100}]

A387111 Number of ways to choose a sequence of distinct positive integers, one in the initial interval of each prime index of n.

Original entry on oeis.org

1, 1, 2, 0, 3, 1, 4, 0, 2, 2, 5, 0, 6, 3, 4, 0, 7, 0, 8, 0, 6, 4, 9, 0, 6, 5, 0, 0, 10, 1, 11, 0, 8, 6, 9, 0, 12, 7, 10, 0, 13, 2, 14, 0, 2, 8, 15, 0, 12, 2, 12, 0, 16, 0, 12, 0, 14, 9, 17, 0, 18, 10, 4, 0, 15, 3, 19, 0, 16, 4, 20, 0, 21, 11, 4, 0, 16, 4, 22

Offset: 1

Gus Wiseman, Aug 18 2025

The initial interval of a nonnegative integer x is the set {1,...,x}.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The axiom of choice says that, given any sequence of nonempty sets, it is possible to choose a sequence containing an element from each. In the strict version, the elements of this sequence must be distinct, meaning none is chosen more than once.

			The prime indices of 75 are (2,3,3), with initial intervals ({1,2},{1,2,3},{1,2,3}), with choices (1,2,3), (1,3,2), (2,1,3), (2,3,1), so a(75) = 4.

Allowing repeated partitions gives A003963.
For constant instead of distinct we have A055396.
For multiset systems see A355529, A355744, A367771, set systems A367901-A367905.
For divisors we have A355739, zeros A355740, strict case of A355731.
For prime factors we have A355741, prime powers A355742, weakly increasing A355745.
For integer partitions we have A387110.
Positions of nonzero terms are A387112 (choosable).
Positions of 0 are A387134 (non-choosable).
A001414 adds up distinct prime divisors, counted by A001221.
A061395 gives greatest prime index.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
A324850 lists numbers divisible by the product of their prime indices.
Cf. A000720, A326841, A335433, A335448, A355733, A355737, A355747, A357980, A383706, A387120, A387133, A387135.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Tuples[Range/@prix[n]],UnsameQ@@#&]],{n,100}]

A387120 Number of ways to choose a different constant integer partition of each prime index of n.

Original entry on oeis.org

1, 1, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 4, 3, 4, 0, 2, 2, 4, 0, 6, 2, 3, 0, 2, 4, 0, 0, 4, 4, 2, 0, 4, 2, 6, 0, 6, 4, 8, 0, 2, 6, 4, 0, 4, 3, 4, 0, 6, 2, 4, 0, 5, 0, 4, 0, 8, 4, 2, 0, 6, 2, 6, 0, 8, 4, 2, 0, 6, 6, 6, 0, 4, 6, 4, 0, 6, 8, 4, 0, 0, 2, 2, 0, 4, 4, 8

Offset: 1

Gus Wiseman, Aug 26 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

			The prime indices of 90 are {1,2,2,3}, with choices:
  ((1),(2),(1,1),(3))
  ((1),(1,1),(2),(3))
  ((1),(2),(1,1),(1,1,1))
  ((1),(1,1),(2),(1,1,1))
so a(90) = 4.

For multiset systems see A355529, set systems A367901.
For not necessarily different choices we have A355731, see A355740.
For divisors instead of constant partitions we have A355739 (also the disjoint case).
For prime factors instead of constant partitions we have A387136.
For all instead of just constant partitions we have A387110, disjoint case A383706.
For initial intervals instead of partitions we have A387111.
For strict instead of constant partitions we have A387115.
Twice partitions of this type are counted by A387179, constant-block case of A296122.
Positions of zero are A387180 (non-choosable), complement A387181 (choosable).
A000041 counts integer partitions, strict A000009.
A003963 multiplies together prime indices.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A000005, A063834, A261049, A299200, A299201, A335433, A335448, A355741, A357977, A387135.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Tuples[Select[IntegerPartitions[#],SameQ@@#&]&/@prix[n]],UnsameQ@@#&]],{n,100}]

A387115 Number of ways to choose a sequence of distinct strict integer partitions, one of each prime index of n.

Original entry on oeis.org

1, 1, 1, 0, 2, 1, 2, 0, 0, 2, 3, 0, 4, 2, 2, 0, 5, 0, 6, 0, 2, 3, 8, 0, 2, 4, 0, 0, 10, 2, 12, 0, 3, 5, 4, 0, 15, 6, 4, 0, 18, 2, 22, 0, 0, 8, 27, 0, 2, 2, 5, 0, 32, 0, 6, 0, 6, 10, 38, 0, 46, 12, 0, 0, 8, 3, 54, 0, 8, 4, 64, 0, 76, 15, 2, 0, 6, 4, 89, 0, 0

Offset: 1

Gus Wiseman, Aug 20 2025

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The axiom of choice says that, given any sequence of nonempty sets, it is possible to choose a sequence containing an element from each. In the strict version, the elements of this sequence must be distinct, meaning none is chosen more than once.

			The prime indices of 15 are (2,3), and there are a(15) = 2 choices:
  ((2),(3))
  ((2),(2,1))
The prime indices of 121 are (5,5), and there are a(121) = 6 choices:
  ((5),(4,1))
  ((5),(3,2))
  ((4,1),(5))
  ((4,1),(3,2))
  ((3,2),(5))
  ((3,2),(4,1))

For divisors instead of partitions we have A355739, see A355740, A355733, A355734.
Allowing repeated partitions gives A357982, see A299200, A357977, A357978.
Twice-partitions of this type are counted by A358914, strict case of A270995.
The disjoint case is A383706.
Allowing non-strict partitions gives A387110, for prime factors A387133.
For initial intervals instead of strict partitions we have A387111.
For constant instead of strict partitions we have A387120.
Positions of 0 are A387176 (non-choosable), complement A387177 (choosable).
A000041 counts integer partitions, strict A000009.
A003963 multiplies together the prime indices of n.
A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
A120383 lists numbers divisible by all of their prime indices.
A289509 lists numbers with relatively prime prime indices.
Cf. A000720, A063834, A261049, A335433, A335448, A355731, A355741, A355742, A355744, A357980.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Tuples[Select[IntegerPartitions[#],UnsameQ@@#&]&/@prix[n]],UnsameQ@@#&]],{n,100}]

A385716 Expansion of 1/((1-x) * (1-13*x))^(3/2).

Original entry on oeis.org

1, 21, 348, 5320, 78135, 1120287, 15805972, 220445316, 3047961735, 41857891075, 571725145992, 7774356136092, 105324231178621, 1422411298153125, 19157947746089520, 257427540725705056, 3451990965984505251, 46205867184493459023, 617482101788090727220, 8239952016851603641320

Offset: 0

Seiichi Manyama, Aug 19 2025

Paolo Xausa, Table of n, a(n) for n = 0..800

Cf. A331516, A385563.

Cf. A340973, A386362.

Module[{x}, CoefficientList[Series[1/((1-x)*(1-13*x))^(3/2), {x, 0, 25}], x]] (* Paolo Xausa, Aug 25 2025 *)

my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-13*x))^(3/2))

n*a(n) = (14*n+7)*a(n-1) - 13*(n+1)*a(n-2) for n > 1.
a(n) = (1/4)^n * Sum_{k=0..n} 13^k * (2*k+1) * (2*(n-k)+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
a(n) = Sum_{k=0..n} 3^k * (2*k+1) * binomial(2*k,k) * binomial(n+2,n-k).
a(n) = Sum_{k=0..n} (-3)^k * 13^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+2,n-k).
a(n) = binomial(n+2,2) * A386362(n).
a(n) = ((n+2)/2) * Sum_{k=0..floor(n/2)} 9^k * 7^(n-2*k) * binomial(n+1,n-2*k) * binomial(2*k+1,k).
a(n) = Sum_{k=0..n} (7/2)^k * (-13/14)^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(k,n-k).
a(n) ~ sqrt(3*n) * 13^(n + 3/2) / (36*sqrt(Pi)). - Vaclav Kotesovec, Aug 21 2025

A385563 Expansion of 1/((1-x) * (1-5*x))^(3/2).

Original entry on oeis.org

1, 9, 60, 360, 2055, 11403, 62132, 334260, 1781415, 9425295, 49581576, 259601004, 1353939405, 7038232425, 36484340400, 188665670880, 973545780195, 5014258620075, 25783103206100, 132378800689800, 678768332410245, 3476164133573505, 17782899991147500

Offset: 0

Seiichi Manyama, Aug 19 2025

Paolo Xausa, Table of n, a(n) for n = 0..1000

Partial sums of A383254.
Cf. A331516, A385716.
Cf. A385728, A385813.
Cf. A002212, A383949.

Module[{a, n}, RecurrenceTable[{a[n] == ((6*n+3)*a[n-1] - 5*(n+1)*a[n-2])/n, a[0] == 1, a[1] == 9}, a, {n, 0, 25}]] (* Paolo Xausa, Aug 21 2025 *)

my(N=30, x='x+O('x^N)); Vec(1/((1-x)*(1-5*x))^(3/2))

n*a(n) = (6*n+3)*a(n-1) - 5*(n+1)*a(n-2) for n > 1.
a(n) = (1/4)^n * Sum_{k=0..n} 5^k * (2*k+1) * (2*(n-k)+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
a(n) = Sum_{k=0..n} (2*k+1) * binomial(2*k,k) * binomial(n+2,n-k).
a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+2,n-k).
a(n) = binomial(n+2,2) * A002212(n+1).
a(n) = ((n+2)/2) * Sum_{k=0..floor(n/2)} 3^(n-2*k) * binomial(n+1,n-2*k) * binomial(2*k+1,k).
a(n) = Sum_{k=0..n} (3/2)^k * (-5/6)^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(k,n-k).
a(n) ~ sqrt(n) * 5^(n + 3/2) / (4*sqrt(Pi)). - Vaclav Kotesovec, Aug 21 2025

A387118 Number of integer partitions of n without choosable initial intervals.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 6, 8, 13, 19, 28, 37, 52, 70, 97, 130, 172, 224, 293, 378, 492, 630, 806, 1018, 1286, 1609, 2019, 2514, 3131, 3874, 4784

Offset: 0

Gus Wiseman, Sep 02 2025

The initial interval of a nonnegative integer x is the set {1,...,x}.

We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.

			The partition y = (2,2,1) has initial intervals ({1,2},{1,2},{1}), which are not choosable, so y is counted under a(5).
The a(2) = 1 through a(8) = 13 partitions:
  (11)  (111)  (211)   (221)    (222)     (511)      (611)
               (1111)  (311)    (411)     (2221)     (2222)
                       (2111)   (2211)    (3211)     (3221)
                       (11111)  (3111)    (4111)     (3311)
                                (21111)   (22111)    (4211)
                                (111111)  (31111)    (5111)
                                          (211111)   (22211)
                                          (1111111)  (32111)
                                                     (41111)
                                                     (221111)
                                                     (311111)
                                                     (2111111)
                                                     (11111111)

The complement is counted by A238873, ranks A387112.
The complement for divisors is A239312, ranks A368110.
For divisors instead of initial intervals we have A370320, ranks A355740.
The complement for prime factors is A370592, ranks A368100.
For prime factors instead of initial intervals we have A370593, ranks A355529.
These partitions have ranks A387113.
For partitions instead of initial intervals we have A387134.
The complement for partitions is A387328.
For strict partitions instead of initial intervals we have A387137, ranks A387176.
The complement for strict partitions is A387178.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A367902 counts choosable set-systems, complement A367903.
A370582 counts sets with choosable prime factors, complement A370583.
Cf. A005703, A052335, A367867, A367901, A367905, A367907, A370585, A370594, A387111.

Table[Length[Select[IntegerPartitions[n],Select[Tuples[Range/@#],UnsameQ@@#&]=={}&]],{n,0,10}]

A387137 Number of integer partitions of n whose parts do not have choosable sets of strict integer partitions.

Original entry on oeis.org

0, 0, 1, 1, 3, 4, 6, 9, 14, 20, 29, 39, 56, 74, 101, 134, 178, 232, 305, 392, 508, 646, 825, 1042, 1317, 1649, 2066, 2567, 3190, 3937, 4859, 5960, 7306, 8914, 10863, 13183, 15984, 19304, 23288, 28003, 33631, 40272, 48166, 57453, 68448, 81352, 96568, 114383

Offset: 0

Gus Wiseman, Sep 02 2025

We say that a sequence of nonempty sets is choosable iff it is possible to choose a different element from each set. For example, ({1,2},{1},{1,3}) is choosable because we have the choice (2,1,3), but ({1},{2},{1,3},{2,3}) is not.
a(n) is the number of integer partitions of n such that it is not possible to choose a sequence of distinct strict integer partitions, one of each part.
Also the number of integer partitions of n with at least one part k whose multiplicity exceeds A000009(k).

			The a(2) = 1 through a(8) = 14 partitions:
  (11)  (111)  (22)    (221)    (222)     (322)      (422)
               (211)   (311)    (411)     (511)      (611)
               (1111)  (2111)   (2211)    (2221)     (2222)
                       (11111)  (3111)    (3211)     (3221)
                                (21111)   (4111)     (3311)
                                (111111)  (22111)    (4211)
                                          (31111)    (5111)
                                          (211111)   (22211)
                                          (1111111)  (32111)
                                                     (41111)
                                                     (221111)
                                                     (311111)
                                                     (2111111)
                                                     (11111111)

The complement for initial intervals is A238873, ranks A387112.
The complement for divisors is A239312, ranks A368110.
Twice-partitions of this type (into distinct strict partitions) are counted by A358914.
For divisors instead of strict partitions we have A370320, ranks A355740.
The complement for prime factors is A370592, ranks A368100.
For prime factors instead of strict partitions we have A370593, ranks A355529.
For initial intervals instead of strict partitions we have A387118, ranks A387113.
For all partitions instead of strict partitions we have A387134, ranks A387577.
These partitions are ranked by A387176.
The complement is counted by A387178, ranks A387177.
The complement for partitions is A387328, ranks A387576.
The version for constant partitions is A387329, ranks A387180.
The complement for constant partitions is A387330, ranks A387181.
A000005 counts divisors.
A000041 counts integer partitions, strict A000009.
A367902 counts choosable set-systems, complement A367903.
Cf. A005703, A052335, A261049, A270995, A276078, A335448, A355535, A367867, A367901, A367905, A383706, A387115.

strptns[n_]:=Select[IntegerPartitions[n],UnsameQ@@#&];
Table[Length[Select[IntegerPartitions[n],Length[Select[Tuples[strptns/@#],UnsameQ@@#&]]==0&]],{n,0,15}]

A387276 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(n+3,k+3) * binomial(2*k+6,k+6).

Original entry on oeis.org

1, 20, 255, 2650, 24521, 210840, 1725234, 13631700, 104993955, 793367300, 5907885412, 43495473840, 317355930255, 2298888740400, 16555878011448, 118661449810320, 847132614218907, 6027874235210700, 42773816956415055, 302816249208061050, 2139537520524710691

Offset: 0

Seiichi Manyama, Aug 24 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Cf. A387275, A387277, A387278.

Cf. A387239, A387273.

[&+[3^(n-k) * Binomial(n+3,k+3) * Binomial(2*k+6,k+6): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Aug 31 2025

Table[Sum[3^(n-k)*Binomial[n+3,k+3]*Binomial[2*k+6,k+6],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Aug 31 2025 *)

a(n) = sum(k=0, n, 3^(n-k)*binomial(n+3, k+3)*binomial(2*k+6, k+6));

n*(n+6)*a(n) = (n+3) * (5*(2*n+5)*a(n-1) - 21*(n+2)*a(n-2)) for n > 1.
a(n) = Sum_{k=0..floor(n/2)} 5^(n-2*k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).
a(n) = [x^n] (1+5*x+x^2)^(n+3).
E.g.f.: exp(5*x) * BesselI(3, 2*x), with offset 3.

A386430 Odd numbers k such that there are no prime factors p of sigma(k) such that p does not divide A003961(k) and the valuation(k, p) is different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

Original entry on oeis.org

1, 3, 7, 15, 21, 27, 31, 33, 57, 69, 87, 91, 93, 105, 127, 141, 177, 189, 195, 217, 231, 237, 273, 285, 301, 381, 399, 447, 465, 483, 495, 513, 567, 573, 597, 609, 627, 651, 717, 775, 819, 837, 861, 889, 903, 987, 1023, 1029, 1149, 1185, 1239, 1311, 1365, 1419, 1431, 1437, 1455, 1497, 1561, 1653, 1659, 1687, 1743

Offset: 1

Antti Karttunen, Aug 22 2025

Conjecture: After the initial 1, and apart from any hypothetical odd perfect numbers, all other terms are in A248150, i.e., sigma(k) == 0 (mod 4). This would imply (with the same caveat), that this sequence has no common terms with A228058 and no squares larger than one. This is true at least for the first 709203 terms (terms in range [1..2^34]).

Terms k such that A162642(k) = 1 are rare: 3, 7, 27, 31, 127, 567, 775, 8191, 27783, 131071, 524287, 2147483647, ... (odd terms of A387160).

			a(386548) = 5919068925 = 3^4 * 5^2 * 7^2 * 11^2 * 17 * 29. sigma(5919068925) = 15355618740 = 2^2 * 3^4 * 5 * 7 * 11^2 * 19^2 * 31. The "don't care primes" is given by A003961(A007947(5919068925))) = 2947945 = 5*7*11*13*19*31, thus only odd prime factor that matters here is 3, which in case has the same exponent (4) in both n = 5919068925 and sigma(n). In a way, this number is very close to satisfying Euler's criterion for odd perfect numbers (A228058), except that it has two unitary prime factors of the form 4k+1, instead of just one, apart from the square factor. Both n/17 and n/29 are in A228058.

Odd terms of A351554.
Cf. A000203, A003961, A056169, A162642, A228058, A248150, A351555, A386424, A387160.
Cf. A349169 (subsequence).

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351555(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); sum(k=1,#f~,if((f[k,1]%2) && 0!=(u%f[k,1]), (valuation(n,f[k,1])!=f[k,2]), 0)); };
isA386430(n) = ((n%2) && (0==A351555(n)));

{k | k odd, A351555(k) = 0}.

cp's OEIS Frontend

A387110 Number of ways to choose a sequence of distinct integer partitions, one of each prime index of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A387111 Number of ways to choose a sequence of distinct positive integers, one in the initial interval of each prime index of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A387120 Number of ways to choose a different constant integer partition of each prime index of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A387115 Number of ways to choose a sequence of distinct strict integer partitions, one of each prime index of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A385716 Expansion of 1/((1-x) * (1-13*x))^(3/2).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A385563 Expansion of 1/((1-x) * (1-5*x))^(3/2).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A387118 Number of integer partitions of n without choosable initial intervals.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A387137 Number of integer partitions of n whose parts do not have choosable sets of strict integer partitions.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A387276 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(n+3,k+3) * binomial(2*k+6,k+6).

Views

Author

Keywords

Links