A078012 -id:A078012 - cp's OEIS frontend

A353502 Numbers with all prime indices and exponents > 2.

1, 125, 343, 625, 1331, 2197, 2401, 3125, 4913, 6859, 12167, 14641, 15625, 16807, 24389, 28561, 29791, 42875, 50653, 68921, 78125, 79507, 83521, 103823, 117649, 130321, 148877, 161051, 166375, 205379, 214375, 226981, 274625, 279841, 300125, 300763, 357911

Offset: 1

Gus Wiseman, May 16 2022

nonn

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 initial terms together with their prime indices:
       1: {}
     125: {3,3,3}
     343: {4,4,4}
     625: {3,3,3,3}
    1331: {5,5,5}
    2197: {6,6,6}
    2401: {4,4,4,4}
    3125: {3,3,3,3,3}
    4913: {7,7,7}
    6859: {8,8,8}
   12167: {9,9,9}
   14641: {5,5,5,5}
   15625: {3,3,3,3,3,3}
   16807: {4,4,4,4,4}
   24389: {10,10,10}
   28561: {6,6,6,6}
   29791: {11,11,11}
   42875: {3,3,3,4,4,4}

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3000 terms from Amiram Eldar)

The version for only parts is A007310, counted by A008483.
The version for <= 2 instead of > 2 is A018256, # of compositions A137200.
The version for only multiplicities is A036966, counted by A100405.
The version for indices and exponents prime (instead of > 2) is:
- listed by A346068
- counted by A351982
- only exponents: A056166, counted by A055923
- only parts: A076610, counted by A000607
The version for > 1 instead of > 2 is A062739, counted by A339222.
The version for compositions is counted by A353428, see A078012, A353400.
The partitions with these Heinz numbers are counted by A353501.
A000726 counts partitions with multiplicities <= 2, compositions A128695.
A001222 counts prime factors with multiplicity, distinct A001221.
A004250 counts partitions with some part > 2, compositions A008466.
A056239 adds up prime indices, row sums of A112798 and A296150.
A124010 gives prime signature, sorted A118914.
A295341 counts partitions with some multiplicity > 2, compositions A335464.
Cf. A000720, A003963, A065483, A114901, A181819, A353503, A353508.

Select[Range[10000],#==1||!MemberQ[FactorInteger[#],{?(#<5&),}|{,?(#<3&)}]&]

Sum_{n>=1} 1/a(n) = Product_{p prime > 3} (1 + 1/(p^2*(p-1))) = (72/95)*A065483 = 1.0154153584... . - Amiram Eldar, May 28 2022

A371209 Number of ordered factorizations of n into factors > 2.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1, 3, 1, 3, 3, 1, 1, 5, 2, 1, 4, 3, 1, 5, 1, 3, 3, 1, 3, 9, 1, 1, 3, 5, 1, 5, 1, 3, 8, 1, 1, 10, 2, 3, 3, 3, 1, 8, 3, 5, 3, 1, 1, 15, 1, 1, 8, 5, 3, 5, 1, 3, 3, 5, 1, 18, 1, 1, 8, 3, 3, 5, 1, 10, 8, 1, 1, 15, 3, 1, 3

Offset: 1

Ilya Gutkovskiy, Mar 15 2024

nonn

			a(12) = 3: 12 = 3*4 = 4*3.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002033, A008483, A074206, A078012, A371211, A371212, A371213.

a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 2, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 87}]

a(1) = 1; a(n) = Sum_{d|n, n/d > 2} a(d).

A065417 Exponents in expansion of rank-2 Artin constant product(1-1/(p^3-p^2), p=prime) as a product zeta(n)^(-a(n)).

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 11, 14, 20, 27, 39, 52, 75, 102, 145, 201, 286, 397, 565, 791, 1123, 1581, 2248, 3173, 4517, 6399, 9112, 12945, 18457, 26270, 37502, 53478, 76416, 109146, 156135, 223301, 319764, 457884, 656288, 940795, 1349671, 1936620

Offset: 1

N. J. A. Sloane, Nov 15 2001

nonn

Inverse Euler transform of A078012. (The inverse of 1-1/(p^3-p^2) is p^2(p-1)/(p^3-p^2-1) = 1-1/(1+p^2-p^3). Setting 1/p=x gives (1-x)/(1-x-x^3), the g.f. of A078012.) - R. J. Mathar, Jul 26 2010

			x^3 + x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + 3*x^9 + 4*x^10 + 6*x^11 + 7*x^12 + ...

Vaclav Kotesovec, Table of n, a(n) for n = 1..5000
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011, sequence gamma_{2,j}^(A).
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
Index entries for sequences related to Artin's conjecture

Cf. A065414.

read("transforms") ;
A078012 := proc(n) option remember; if n <3 then op(n+1,[1,0,0]) ; else procname(n-1)+procname(n-3) ; end if; end proc:
a078012 := [seq(A078012(n),n=1..80)] ; EULERi(%) ;
# R. J. Mathar, Jul 26 2010

A078012[n_] := A078012[n] = If[n<3, {1, 0, 0}[[n+1]], A078012[n-1] + A078012[n-3]]; a078012 = Array[A078012, m = 80];
s = {}; For[i = 1, i <= m, i++, AppendTo[s, i*a078012[[i]] - Sum[s[[d]] * a078012[[i-d]], {d, i-1}]]]; Table[Sum[If[Divisible[i, d], MoebiusMu[i/d ], 0]*s[[d]], {d, 1, i}]/i, {i, m}] (* Jean-François Alcover, Apr 15 2016, after R. J. Mathar *)

a(n) ~ r^n / n, where r = A092526 = 1.465571231876768... - Vaclav Kotesovec, Jun 13 2020

More terms from R. J. Mathar, Jul 26 2010

A353508 Number of integer compositions of n with no ones or runs of length 1.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 8, 2, 11, 4, 21, 5, 37, 12, 57, 25, 104, 38, 177, 79, 292, 149, 513, 251, 876, 482, 1478, 871, 2562, 1533, 4387, 2815, 7473, 5036, 12908, 8935, 22135, 16085, 37940, 28611, 65422, 50731, 112459, 90408, 193386, 160119, 333513

Offset: 0

Gus Wiseman, May 17 2022

nonn

			The a(0) = 1 through a(14) = 11 compositions (empty columns indicated by dots, 0 is the empty composition):
  0  .  .  .  22  .  33   .  44    333  55     .  66      22333  77
                     222     2222       2233      444     33322  2255
                                        3322      2244           3344
                                        22222     3333           4433
                                                  4422           5522
                                                  22233          22244
                                                  33222          44222
                                                  222222         222233
                                                                 223322
                                                                 332222
                                                                 2222222

Alois P. Heinz, Table of n, a(n) for n = 0..1000

The version for partitions is A339222.
Compositions counted by their run-lengths:
- For run-lengths <= 1 we have A003242, ranked by A333489.
- For run-lengths = 2 we have A003242 aerated.
- For run-lengths > 1 we have A114901, ranked by A353427.
- For run-lengths <= 2 we have A128695 matching A335464.
- For run-lengths > 2 we have A353400, partitions A100405.
- For run-lengths all prime we have A353401.
- For run-lengths and parts > 2 we have A353428.
A008466 counts compositions with some part > 2.
A011782 counts compositions.
A106356 counts compositions by number of adjacent equal parts.
A261983 counts non-anti-run compositions.
A274174 counts compositions with equal parts contiguous.
Cf. A005811, A078012, A238279, A329739, A333755, A351013, A353390.

b:= proc(n,h) option remember; `if`(n=0, 1, add(
     `if`(i<>h, add(b(n-i*j, i), j=2..n/i), 0), i=2..n/2))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..60);  # Alois P. Heinz, May 17 2022

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MemberQ[#,1]&&!MemberQ[Length/@Split[#],1]&]],{n,0,15}]

a(41)-a(52) from Alois P. Heinz, May 17 2022

A360709 Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.

Original entry on oeis.org

1, 0, 0, 1, 1, 1, 2, 5, 13, 34, 90, 247, 720, 2256, 7568, 26814, 98982, 377541, 1484254, 6021789, 25271173, 109850447, 494355359, 2298362532, 11008133629, 54175202125, 273460921605, 1414449612648, 7494262602464, 40669492399396

Offset: 0

Seiichi Manyama, Feb 17 2023

nonn

Winston de Greef, Table of n, a(n) for n = 0..692

Cf. A080108, A360708.

Cf. A078012, A360707.

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x^3/(1-k*x))^k))

a(n) = if(n==0, 1, sum(k=1, n\3, k^(n-3*k)*binomial(n-2*k-1, k-1)));

a(n) = Sum_{k=1..floor(n/3)} k^(n-3*k) * binomial(n-2*k-1,k-1) for n > 0.

A323949 Number of set partitions of {1, ..., n} with no block containing three distinct cyclically successive vertices.

Original entry on oeis.org

1, 1, 2, 4, 10, 36, 145, 631, 3015, 15563, 86144, 508311, 3180930, 21018999, 146111543, 1065040886, 8117566366, 64531949885, 533880211566, 4587373155544, 40865048111424, 376788283806743, 3590485953393739, 35312436594162173, 357995171351223109, 3736806713651177702

Offset: 0

Gus Wiseman, Feb 10 2019

nonn

Cyclically successive means 1 is a successor of n.

			The a(1) = 1 through a(4) = 10 set partitions:
  {{1}}  {{1,2}}    {{1},{2,3}}    {{1,2},{3,4}}
         {{1},{2}}  {{1,2},{3}}    {{1,3},{2,4}}
                    {{1,3},{2}}    {{1,4},{2,3}}
                    {{1},{2},{3}}  {{1},{2},{3,4}}
                                   {{1},{2,3},{4}}
                                   {{1,2},{3},{4}}
                                   {{1},{2,4},{3}}
                                   {{1,3},{2},{4}}
                                   {{1,4},{2},{3}}
                                   {{1},{2},{3},{4}}

Alois P. Heinz, Table of n, a(n) for n = 0..250

Cf. A000085, A000110, A000126, A000296, A000325, A001610, A001644, A078012, A169985.

Cf. A306351, A306357, A323950, A323951, A323953, A323954, A323955, A323956.

spsu[,{}]:={{}};spsu[foo,set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,_}];
Table[Length[spsu[Select[Subsets[Range[n]],Select[Partition[Range[n],3,1,1],Function[ed,UnsameQ@@ed&&Complement[ed,#]=={}]]=={}&],Range[n]]],{n,8}]

a(12)-a(25) from Alois P. Heinz, Feb 10 2019

A371243 Number of factorizations of n into factors > 2.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 3, 2, 1, 3, 1, 2, 2, 1, 2, 5, 1, 1, 2, 3, 1, 3, 1, 2, 4, 1, 1, 5, 2, 2, 2, 2, 1, 4, 2, 3, 2, 1, 1, 6, 1, 1, 4, 4, 2, 3, 1, 2, 2, 3, 1, 7, 1, 1, 4, 2, 2, 3, 1, 5, 5, 1, 1, 6, 2, 1, 2, 3, 1, 7, 2, 2, 2, 1, 2, 7, 1, 2, 4, 5, 1, 3, 1, 3, 5

Offset: 1

Ilya Gutkovskiy, Mar 16 2024

nonn

			a(24) = 3: 24 = 3*8 = 4*6.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A001055, A008483, A078012, A371209, A371244, A371245.

A371243(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>2)&&(d<=m), s += A371243(n/d, d))); (s)); \\ Antti Karttunen, Nov 28 2024

Dirichlet g.f.: Product_{k>=3} 1 / (1 - k^(-s)).

More terms from Antti Karttunen, Nov 28 2024

A277627 Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 column k lists two zeros followed by the partial sums of column k-1.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 3, 5, 1, 0, 0, 0, 0, 0, 0, 0, 6, 6, 1, 0, 0, 0, 0, 0, 0, 0, 1, 10, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 15, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 21, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20, 28, 10, 1

Offset: 0

Paul Curtz, Oct 24 2016

In other words, for n > 0 the column k lists 2*k+1 zeros together with the partial sums of the positive terms of column k-1. - Omar E. Pol, Oct 25 2016
Comments from the author:
1) ZSPEC =
  0, 0, 0, 0, 0, 0, 0, 0, ...
  1, 0, 0, 0, 0, 0, 0, 0, ...
  1, 0, 0, 0, 0, 0, 0, 0, ...
  1, 1, 0, 0, 0, 0, 0, 0, ...
  1, 2, 0, 0, 0, 0, 0, 0, ...
  1, 3, 1, 0, 0, 0, 0, 0, ...
  1, 4, 3, 0, 0, 0, 0, 0, ...
  1, 5, 6, 1, 0, 0, 0, 0, ...
etc.
The columns are the autosequences of the first kind of the title (column 1: 0, 0, followed by A001477(n); column 2: 0, 0, 0, 0, followed by A000217(n), etc) .
The positive terms are the Pascal triangle written by diagonals (A011973).
First column: A060576(n+1). Or A057427(n), n>-1, thanks to Omar E. Pol.
Row sums: A000045(n), autosequence of the first kind.
Alternated row sums and subtractions: 0, 1, 1, 0, -1, -1, 0 = A128834(n), autosequence of the first kind.
Antidiagonal sums: 0, 1, 1, 1, 2, 3, 4, 6, ... = A078012(n+2).
Application.
Numbers in triangle leading to the Genocchi numbers -A226158(n).
We multiply the columns of ZSPEC by d(n) = 1, -1, 2, -8, 56, -608, ... from A005439.
Hence, with only the first 0,
  0,
  1,
  1,
  1, -1,
  1, -2,
  1, -3,  2,
  1, -4,  6,
  1, -5, 12,   -8,
  1, -6, 20,  -32,
  1, -7, 30,  -80,  56,
  1, -8, 42, -160, 280,
  etc.
The row sums is -A226158(n).
2) Now consider the case of the autosequences of the second kind.
First step.
            2, 1, 1,  1,  1,  1, ...        = A054977(n)
      0, 0, 2, 3, 4,  5,  6,  7, ...        = A199969(n) with offset 0
0, 0, 0, 0, 2, 5, 9, 14, 20, 27, ...        see A000096
etc.
The positive terms are ASPEC in A191302. By triangle, they are either A029653(n) with A029653(0) = 2 instead of 1 or A029635(n).
Second step. YSPEC =
  2, 0,  0, 0, 0, 0, ...
  1, 0,  0, 0, 0, 0, ...
  1, 2,  0, 0, 0, 0, ...
  1, 3,  0, 0, 0, 0, ...
  1, 4,  2, 0, 0, 0, ...
  1, 5,  5, 0, 0, 0, ...
  1, 6,  9, 2, 0, 0, ...
  1, 7, 14, 7, 0, 0, ...
  etc.
Diagonals by triangle: A029635(n).
This is the companion to ZSPEC.
Row sums: A000032(n), autosequence of the second kind.
Alternated row sums and subtractions: period 6 repeat 2, 1, -1, -2, -1, 1 = A087204(n), autosequence of the second kind.
Application.
Numbers in triangle leading to A230324(n), a companion to -A226158(n).
We multiply the columns of YSPEC by d(n) 1, -1, 2, -8, 56, ... (see above).
Hence, without zeros:
  2,
  1,
  1, -2,
  1, -3,
  1, -4,  4,
  1, -5, 10,
  1, -6, 18,  -16,
  1, -7, 28,  -56,
  1, -8, 40, -128, 112,
  1, -9, 54, -240, 504,
  etc.
The row sum is A230324(n).

G. C. Greubel, Table of n, a(n) for the first 25 antidiagonals, flattened
OEIS Wiki, Autosequence

Cf. A011973 (without 0's), A007318 (Pascal's triangle).
Cf. A000045 (row sums), A078012 (antidiagonal sums).
Columns: A060576 or A057427 (k=0), A001477 (k=1), A000217 (k=2).
Cf. A000004, A000012, A000027, A000032, A005439, A029635, A029653, A054977, A087204, A128834, A191302, A199969, A226158, A230324.

kMax = 13; col[0] = Join[{0}, Array[1&, kMax]]; col[k_] := col[k] = Join[{0, 0}, col[k-1][[1 ;; -3]] // Accumulate]; T[n_, k_] := col[k][[n+1]]; Table[T[n-k, k], {n, 0, kMax}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 15 2016 *)

Better definition from Omar E. Pol, Oct 25 2016

A353501 Number of integer partitions of n with all parts and all multiplicities > 2.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 3, 0, 0, 6, 2, 0, 6, 3, 2, 9, 2, 5, 11, 3, 5, 18, 6, 4, 20, 13, 8, 26, 10, 17, 37, 14, 16, 51, 23, 24, 58, 38, 32, 75, 44, 52, 100, 52, 59, 143, 75, 77, 159, 114, 112, 203, 132, 154, 266, 175

Offset: 0

Gus Wiseman, May 16 2022

nonn

			The a(n) partitions for selected n (A = 10):
  n=9:   n=12:   n=21:      n=24:       n=30:
------------------------------------------------------
  (333)  (444)   (777)      (888)       (AAA)
         (3333)  (444333)   (6666)      (66666)
                 (3333333)  (444444)    (555555)
                            (555333)    (666444)
                            (4443333)   (777333)
                            (33333333)  (6663333)
                                        (55533333)
                                        (444333333)
                                        (3333333333)

The version for only parts > 2 is A008483.
The version for only multiplicities > 2 is A100405.
The version for parts and multiplicities > 1 is A339222, ranked by A062739.
For prime parts and multiplicities we have A351982, compositions A353429.
The version for compositions is A353428 (partial A078012, A353400).
These partitions are ranked by A353502.
A000726 counts partitions with all mults <= 2, compositions A128695.
A004250 counts partitions with some part > 2, compositions A008466.
A137200 counts compositions with all parts and run-lengths <= 2.
Cf. A003242, A047966, A055923, A098859, A114901, A325534, A333755, A335464.

Table[Length[Select[IntegerPartitions[n],Min@@#>2&&Min@@Length/@Split[#]>2&]],{n,0,30}]

A118645 Number of binary strings of length n such that there exist three consecutive digits where at least two of them are 1's.

Original entry on oeis.org

0, 0, 1, 4, 10, 23, 51, 109, 228, 471, 964, 1960, 3967, 8003, 16107, 32362, 64941, 130200, 260866, 522415, 1045831, 2093129, 4188408, 8379967, 16764552, 33535872, 67081663, 134177863, 268377031, 536785286, 1073616333, 2147299732

Offset: 0

Tanya Khovanova, May 10 2006

We set a(2) = 1 by convention; there is one string of length 2 which has two consecutive 1's, namely 11. This also makes various formulas simpler.
For n>=3, a(n) = 2^n - the sum of all terms in the (n-3)rd power of the 4 X 4 matrix [[1 1 0 0] [0 0 1 0] [0 0 0 1] [1 1 0 0]] because this matrix represents the transitions from the state where the last three bits are 000, 001, 010, 100 to the state after the next bit, always avoiding two 1's out of the last three bits. - Joshua Zucker, Aug 04 2006
Complementary to A048625 which starts 4,6,9,13,19,28,41,60,88,129,189. For n >= 3, a(n) + A048625(n-3) = 2^n. A048625 is a subsequence of A000930, A068921 and A078012. All of them satisfy the recurrence a(n) = a(n-1) + a(n-3). - Tanya Khovanova, Aug 22 2006

			a(4) = 10 because we have: 0011, 0101, 0110, 0111, 1010, 1011, 1100, 1101, 1110, 1111. - _Geoffrey Critzer_, Jan 19 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-2).

nn=31;r=Solve[{s==1+x s+x b,a==x s,b==x a,c==x a+x b+2x c},{s,a,b,c}]; CoefficientList[Series[c/.r,{x,0,nn}],x] (* Geoffrey Critzer, Jan 19 2014 *)
LinearRecurrence[{3,-2,1,-2},{0,0,1,4},40] (* Harvey P. Dale, Dec 15 2014 *)

x='x+O('x^50); concat([0,0], Vec((x^3 + x^2)/(2*x^4 - x^3 + 2*x^2 - 3*x + 1))) \\ G. C. Greubel, May 02 2017

a(n) = 3*2^(n-3) + a(n-1) + a(n-3) for n >= 3. - Tanya Khovanova, Aug 22 2006
From R. J. Mathar, Oct 03 2011: (Start)
G.f.: (x^3 + x^2)/(2*x^4 - x^3 + 2*x^2 - 3*x + 1).
G.f.: x^2 * (x+1)/((2*x-1)*(x^3+x-1)).
a(n) = 2^n - A000930(n+2). (End)

More terms from Joshua Zucker, Aug 04 2006

Edited by Franklin T. Adams-Watters, Sep 30 2011

cp's OEIS Frontend

A353502 Numbers with all prime indices and exponents > 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A371209 Number of ordered factorizations of n into factors > 2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A065417 Exponents in expansion of rank-2 Artin constant product(1-1/(p^3-p^2), p=prime) as a product zeta(n)^(-a(n)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A353508 Number of integer compositions of n with no ones or runs of length 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A360709 Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula

A323949 Number of set partitions of {1, ..., n} with no block containing three distinct cyclically successive vertices.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A371243 Number of factorizations of n into factors > 2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

A277627 Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 column k lists two zeros followed by the partial sums of column k-1.

Views