A002409 -id:A002409 - cp's OEIS frontend

A140406 a(n) = binomial(n+6, 6)*8^n.

1, 56, 1792, 43008, 860160, 15138816, 242221056, 3598712832, 50381979648, 671759728640, 8598524526592, 106309030510592, 1275708366127104, 14915974742409216, 170468282770391040, 1909244767028379648, 21001692437312176128, 227312435792084729856

Offset: 0

Zerinvary Lajos, Jun 16 2008

With a different offset, number of n-permutations (n >= 6) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's.
If n=6 then a(0)=1.
Example: a(1)=56 because we have
uuuuuup, uuuuupu, uuuupuu, uuupuuu, uupuuuu, upuuuuu, puuuuuu,
uuuuuur, uuuuuru, uuuuruu, uuuruuu, uuruuuu, uruuuuu, ruuuuuu,
uuuuuus, uuuuusu, uuuusuu, uuusuuu, uusuuuu, usuuuuu, suuuuuu,
uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu,
uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu,
uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu,
uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu,
uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu.

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (56,-1344,17920,-143360,688128,-1835008,2097152).

Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140405.

[8^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

Maple
```
seq(binomial(n+6,6)*8^n,n=0..17);
```

Table[Binomial[n+6,6]8^n,{n,0,20}] (* or *) LinearRecurrence[ {56,-1344,17920,-143360,688128,-1835008,2097152},{1,56,1792,43008,860160,15138816,242221056},20] (* Harvey P. Dale, Dec 15 2011 *)

a(n)=binomial(n+6,6)<<(3*n) \\ Charles R Greathouse IV, Dec 15 2011

G.f.: 1/(1-8*x)^7. - Zerinvary Lajos, Aug 06 2008
a(n) = 56*a(n-1) - 1344*a(n-2) + 17920*a(n-3) - 143360*a(n-4) + 688128*a(n-5) - 1835008*a(n-6) + 2097152*a(n-7). - Harvey P. Dale, Dec 15 2011
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 538628/5 - 806736*log(8/7).
Sum_{n>=0} (-1)^n/a(n) = 2834352*log(9/8) - 1669188/5. (End)

A162007 Third left hand column of the EG1 triangle A162005.

Original entry on oeis.org

1, 270, 36096, 4766048, 704357760, 120536980224, 24060789342208, 5590122715250688, 1503080384197754880, 464520829174515630080, 163839204411117787938816, 65500849343294249018327040

Offset: 3

Johannes W. Meijer, Jun 27 2009

Third left hand column of the EG1 triangle A162005.
Other left hand columns are A000182 and A162006.
Related to A094665, A083061 and A156919.
A000079, A036289 and A100381 appear in the a(n, 3) formula.
A001789, A003472, A054849, A002409, A054851, A140325 and A140354 (scaled by 2^(m-1)) appear one by one in the a(n, m) formulas for m= 4 and higher .

nmax := 14; mmax := nmax: imax := nmax: T1(0, x) := 1: T1(0, x+1) := 1: for i from 1 to imax do T1(i, x) := expand((2*x+1)*(x+1)*T1(i-1, x+1) - 2*x^2*T1(i-1, x)): dx := degree(T1(i, x)): for k from 0 to dx do c(k) := coeff(T1(i, x), x, k) od: T1(i, x+1) := sum(c(j1)*(x+1)^(j1), j1 = 0..dx): od: for i from 0 to imax do for j from 0 to i do A083061(i, j) := coeff(T1(i, x), x, j) od: od: for n from 0 to nmax do for k from 0 to n do A094665(n+1, k+1) := A083061(n, k) od: od: A094665(0, 0) := 1: for n from 1 to nmax do A094665(n, 0) := 0 od: for m from 1 to mmax do A156919(0, m) := 0 end do: for n from 0 to nmax do A156919(n, 0) := 2^n end do: for n from 1 to nmax do for m from 1 to mmax do A156919(n, m) := (2*m+2)*A156919(n-1, m) + (2*n-2*m+1) * A156919(n-1, m-1) end do end do: m:=3; for n from m to nmax do a(n, m) := sum((-1)^(m-p1-1)*sum(2^(n-q-1)*binomial(n-q-1, m-p1-1) * A094665(n-1, q) * A156919(q, p1), q=1..n-m+p1), p1=0..m-1) od: seq(a(n, m), n = m..nmax);
# Maple program edited by Johannes W. Meijer, Sep 25 2012

a(n) = sum((-1)^(m-p-1)*sum(2^(n-q-1)*binomial(n-q-1,m-p-1)*A094665(n-1,q)* A156919(q,p),q=1..n-m+p), p=0..m-1) with m = 3.

A130812 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,...n).

Original entry on oeis.org

64, 448, 1792, 5376, 13440, 29568, 59136, 109824, 192192, 320320, 512512, 792064, 1188096, 1736448, 2480640, 3472896, 4775232, 6460608, 8614144, 11334400, 14734720, 18944640, 24111360, 30401280, 38001600, 47121984, 57996288, 70884352, 86073856, 103882240

Offset: 6

Milan Janjic, Jul 16 2007

Number of n permutations (n>=6) of 3 objects u,v,z, with repetition allowed, containing n-6 u's. Example: if n=6 then n-6 =(0) zero u, a(1)=64. - Zerinvary Lajos, Aug 05 2008

a(n) is the number of 5-dimensional elements in an n-cross polytope where n>=6. - Patrick J. McNab, Jul 06 2015

Vincenzo Librandi, Table of n, a(n) for n = 6..1000
Milan Janjic, Two Enumerative Functions
Eric Weisstein's World of Mathematics, Cross Polytope

Cf. A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809, A130810, A130811. - Zerinvary Lajos, Aug 05 2008

[Binomial(2*n,6)+Binomial(n,2)*Binomial(2*n-4,2)- n*Binomial(2*n-2,4)-Binomial(n,3): n in [6..40]]; // Vincenzo Librandi, Jul 09 2015

a:=n->binomial(2*n,6)+binomial(n,2)*binomial(2*n-4,2)-n*binomial(2*n-2,4)-binomial(n,3);
seq(binomial(n,n-6)*2^6,n=6..32); # Zerinvary Lajos, Dec 07 2007
seq(binomial(n+5, 6)*2^6, n=1..22); # Zerinvary Lajos, Aug 05 2008

CoefficientList[Series[64/(1-x)^7,{x,0,30}],x] (* Vincenzo Librandi, Mar 21 2012 *)

a(n) = binomial(2*n,6) + binomial(n,2)*binomial(2*n-4,2) - n*binomial(2*n-2,4) - binomial(n,3).
a(n) = C(n,n-6)*2^6, n>=6. - Zerinvary Lajos, Dec 07 2007
G.f.: 64*x^6/(1-x)^7. - Colin Barker, Mar 20 2012

A172242 Number of 10-D hypercubes in an n-dimensional hypercube.

Original entry on oeis.org

1, 22, 264, 2288, 16016, 96096, 512512, 2489344, 11202048, 47297536, 189190144, 722362368, 2648662016, 9372188672, 32133218304, 107110727680, 348109864960, 1105760747520, 3440144547840, 10501493882880, 31504481648640

Offset: 10

Zerinvary Lajos, Jan 29 2010

With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly ten (10) u's.

Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (22,-220,1320,-5280,14784,-29568,42240,-42240,28160,-11264,2048).

Cf. A001788, A001789, A003472, A038207, A054849, A002409, A140325, A054851, A140354.

Table[Binomial[n + 10, 10]*2^n, {n, 0, 22}]

[lucas_number2(n, 2, 0)*binomial(n,10)/2^10 for n in range(10, 31)] # Zerinvary Lajos, Feb 05 2010

a(n) = A038207(n,10).
a(n) = binomial(n,10)*2^(n-10). [Corrected by R. J. Mathar, Feb 21 2010]
G.f.: -x^10/(2*x-1)^11. - Colin Barker, Nov 11 2012
a(n) = Sum_{i=10..n} binomial(i,10)*binomial(n,i). Example: for n=15, a(15) = 1*3003 + 11*1365 + 66*455 + 286*105 + 1001*15 + 3003*1 = 96096. - Bruno Berselli, Mar 23 2018
From Amiram Eldar, Jan 07 2022: (Start)
Sum_{n>=10} 1/a(n) = 1879/126 - 20*log(2).
Sum_{n>=10} (-1)^n/a(n) = 393660*log(3/2) - 20111419/126. (End)

A130811 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 5-subsets of X containing none of X_i, (i=1,...n).

Original entry on oeis.org

32, 192, 672, 1792, 4032, 8064, 14784, 25344, 41184, 64064, 96096, 139776, 198016, 274176, 372096, 496128, 651168, 842688, 1076768, 1360128, 1700160, 2104960, 2583360, 3144960, 3800160, 4560192, 5437152, 6444032, 7594752, 8904192

Offset: 5

Milan Janjic, Jul 16 2007

Number of n permutations (n>=5) of 3 objects u,v,z, with repetition allowed, containing n-5 u's. Example: if n=5 then n-5 =(0) zero u, a(1)=32. - Zerinvary Lajos, Aug 05 2008

a(n) is the number of 4-dimensional elements in an n-cross polytope where n>=5. - Patrick J. McNab, Jul 06 2015

Milan Janjic, Two Enumerative Functions
Eric Weisstein's World of Mathematics, Cross Polytope

Cf. A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809, A130810. - Zerinvary Lajos, Aug 05 2008

[Binomial(n,n-5)*2^5: n in [5..40]]; // Vincenzo Librandi, Jul 09 2015

a:=n->binomial(2*n,5)+(2*n-4)*binomial(n,2)-n*binomial(2*n-2,3)
seq(binomial(n,n-5)*2^5,n=5..34); # Zerinvary Lajos, Dec 07 2007
seq(binomial(n+4, 5)*2^5, n=1..22); # Zerinvary Lajos, Aug 05 2008

Table[Binomial[2 n, 5] + (2 n - 4) Binomial[n, 2] - n Binomial[2 n - 2, 3], {n, 5, 40}] (* Vincenzo Librandi, Jul 09 2015 *)

a(n) = binomial(2*n,5) + (2*n-4)*binomial(n,2) - n*binomial(2*n-2,3).
a(n) = C(n,n-5)*2^5, for n>=5. - Zerinvary Lajos, Dec 07 2007
G.f.: 32*x^5/(1-x)^6. - Colin Barker, Apr 14 2012

A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 14, 112, 8, 672, 144, 3360, 1440, 45, 14784, 10560, 990, 59136, 63360, 11880, 220, 219648, 329472, 102960, 5720, 768768, 1537536, 720720, 80080, 1001, 2562560, 6589440, 4324320, 800800, 30030, 8200192, 26357760, 23063040

Offset: 6

Stanislav Sykora, Jun 13 2012

For a general discussion, please see A213343.
This a(n) is for sextuple-quantum transitions (q = 6).
It lists the flattened triangle T(6;N,k) with rows N = 6,7,... and columns k = 0..floor((N-6)/2).

			Starting rows of the triangle:
   N | k = 0, 1, ..., floor((N-6)/2)
   6 |    1
   7 |   14
   8 |  112    8
   9 |  672  144
  10 | 3360 1440 45

See A213343

Stanislav Sykora, Table of n, a(n) for n = 6..2309
Stanislav Sykora, T(6;N,k) with rows N = 6..100 and columns k = 0..floor((N-6)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Cf. A051288 (q=0), A213343 to A213347 (q=1 to 5), A213349 to A213352 (q=7 to 10).

Cf. A002409 (first column, with offset 6), A004312 (row sums).

With[{q = 6}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, q, q + 10}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 20 2019 *)

PARI
```
See A213343; set thisq = 6
```

Set q = 6 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

A140405 a(n) = binomial(n+6, 6)*5^n.

Original entry on oeis.org

1, 35, 700, 10500, 131250, 1443750, 14437500, 134062500, 1173046875, 9775390625, 78203125000, 604296875000, 4532226562500, 33120117187500, 236572265625000, 1656005859375000, 11385040283203125, 77016448974609375, 513442993164062500, 3377914428710937500

Offset: 0

Zerinvary Lajos, Jun 16 2008

With a different offset, number of n-permutations (n>=6) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's.
If n=6 then a(0)=1.
Example: a(1)=35 because we have
uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu,
uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu,
uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu,
uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu,
uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu.

Index entries for linear recurrences with constant coefficients, signature (35,-525,4375,-21875,65625,-109375,78125).

Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140406.

Maple
```
seq(binomial(n+6,6)*5^n,n=0..18);
```

Table[Binomial[n+6,6]5^n,{n,0,20}] (* Harvey P. Dale, Dec 03 2017 *)

G.f.: 1/(1-5*x)^7. - Zerinvary Lajos, Aug 06 2008
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 6856 - 30720*log(5/4).
Sum_{n>=0} (-1)^n/a(n) = 233280*log(6/5) - 42531. (End)

A372868 Irregular triangle read by rows: T(n,k) is the number of flattened Catalan words of length n with exactly k runs of weak ascents, with 1 <= k <= ceiling(n/2).

Original entry on oeis.org

1, 2, 4, 1, 8, 6, 16, 24, 1, 32, 80, 10, 64, 240, 60, 1, 128, 672, 280, 14, 256, 1792, 1120, 112, 1, 512, 4608, 4032, 672, 18, 1024, 11520, 13440, 3360, 180, 1, 2048, 28160, 42240, 14784, 1320, 22, 4096, 67584, 126720, 59136, 7920, 264, 1, 8192, 159744, 366080, 219648, 41184, 2288, 26

Offset: 1

Stefano Spezia, May 15 2024

With offset 0 for the variable k, T(n,k) is the number of flattened Catalan words of length n with exactly k peaks. In such case, T(4,1) = 6 corresponds to 6 flattened Catalan words of length 4 with 1 peak: 0010, 0100, 0110, 0101, 0120, and 0121. See Baril et al. at page 20.

			The irregular triangle begins:
    1;
    2;
    4,    1;
    8,    6;
   16,   24,    1;
   32,   80,   10;
   64,  240,   60,   1;
  128,  672,  280,  14;
  256, 1792, 1120, 112, 1;
  ...
T(4,2) = 6 since there are 6 flattened Catalan words of length 4 with 2 runs of weak ascents: 0010, 0100, 0101, 0110, 0120, and 0121.

Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See pp. 8-9.

Cf. A000079, A001788, A002409, A003472, A007051 (row sums), A110654 (row lengths), A140325, A172242.

Cf. A372852, A372972.

T[n_,k_]:=SeriesCoefficient[(1-2x)*x*y/(1-4*x+4*x^2-x^2*y),{x,0,n},{y,0,k}]; Table[T[n,k],{n,14},{k,Ceiling[n/2]}] //Flatten (* or *)
T[n_,k_]:=2^(n-2k+1)Binomial[n-1,2k-2]; Table[T[n,k],{n,14},{k,Ceiling[n/2]}]

G.f.: (1-2*x)*x*y/(1 - 4*x + 4*x^2 - x^2*y).
T(n,k) = 2^(n-2*k+1)*binomial(n-1, 2*k-2).
T(n,1) = A000079(n-1).
T(n,2) = A001788(n-2).
T(n,3) = A003472(n-1).
T(n,4) = A002409(n-7).
T(n,5) = A140325(n-9).
T(n,6) = A172242(n-1).
Sum_{k>=0} T(n,k) = A007051(n-1).

A119886 a(n) = 20a(n-2) - 64a(n-4).

Original entry on oeis.org

1, 59, 2416, 6230, 47680, 120824, 798976, 2017760, 12928000, 32622464, 207425536, 523312640, 3321118720, 8378415104, 53147140096, 134076293120, 850391203840, 2145307295744, 13606407110656, 34325263155200, 217703105167360, 549205596176384, 3483252048265216

Offset: 0

Roger L. Bagula, Aug 09 2006

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,20,0,-64).

Cf. A060595, A060638, A002409, A099193, A000937, A099195.

M = {{0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0}} v[1] = Table[Fibonacci[n], {n, 1, 16}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
(* Second program: *)
A = SparseArray[{{1, 8} -> 1, Band[{1, 4}] -> 1, Band[{1, 2}, {3, 4}] -> 1, Band[{5, 6}, {7, 8}] -> 1}, {8, 8}]; M = ArrayFlatten[{{A+Transpose[A], IdentityMatrix[8]}, {IdentityMatrix[8], A+Transpose[A]}}]; v[1] = Array[ Fibonacci, 16]; v[n_] := v[n] = M.v[n-1]; A119886 = Array[v, 50][[All, 1]] (* Jean-François Alcover, Feb 05 2017 *)
LinearRecurrence[{0,20,0,-64},{1,59,2416,6230,47680},30] (* Harvey P. Dale, Sep 06 2024 *)

Vec(-(576*x^4-5050*x^3-2396*x^2-59*x-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)) + O(x^30)) \\ Colin Barker, Feb 05 2017

G.f.: -(576*x^4-5050*x^3-2396*x^2-59*x-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)). - Colin Barker, Nov 17 2012

a(n) = 2^(n-4)*(-3266 + 585*(-2)^n + 258*(-1)^n + 2583*2^n) for n>0. - Colin Barker, Feb 05 2017

New name from Joerg Arndt, Feb 05 2017

A130813 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 7-subsets of X containing none of X_i, (i=1,...n).

Original entry on oeis.org

128, 1024, 4608, 15360, 42240, 101376, 219648, 439296, 823680, 1464320, 2489344, 4073472, 6449664, 9922560, 14883840, 21829632, 31380096, 44301312, 61529600, 84198400, 113667840, 151557120, 199779840, 260582400, 336585600, 430829568

Offset: 7

Milan Janjic, Jul 16 2007

nonn

Number of n permutations (n>=7) of 3 objects u,v,z, with repetition allowed, containing n-7 u's. Example: if n=7 then n-7 =(0) zero u, a(1)=128. - Zerinvary Lajos, Aug 05 2008

a(n) is the number of 6-dimensional elements in an n-cross polytope where n>=7. - Patrick J. McNab, Jul 06 2015

Milan Janjic, Two Enumerative Functions
Eric Weisstein's World of Mathematics, Cross Polytope

Cf. A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809, A130810, A130811, A130812. - Zerinvary Lajos, Aug 05 2008

Cf. A000580.

[Binomial(n,n-7)*2^7: n in [7..40]]; // Vincenzo Librandi, Jul 09 2015

a:=n->binomial(2*n,7)+binomial(n,2)*binomial(2*n-4,3)-n*binomial(2*n-2,5)-(2*n-6)*binomial(n,3);
seq(binomial(n,n-7)*2^7,n=7..32); # Zerinvary Lajos, Dec 07 2007
seq(binomial(n+6, 7)*2^7, n=1..22); # Zerinvary Lajos, Aug 05 2008

Table[Binomial[n, n - 7] 2^7, {n, 7, 40}] (* Vincenzo Librandi, Jul 09 2015 *)

a(n) = binomial(2*n,7) + binomial(n,2)*binomial(2*n-4,3) - n*binomial(2*n-2,5) - (2*n-6)*binomial(n,3).
a(n) = C(n,n-7)*2^7, n>=7. - Zerinvary Lajos, Dec 07 2007
G.f.: 128*x^7/(1-x)^8. - Colin Barker, Mar 18 2012
a(n) = 128*A000580(n). a(n+1) = 2*(n+1)*a(n)/(n-6) for n >= 7. - Robert Israel, Jul 08 2015

cp's OEIS Frontend

A140406 a(n) = binomial(n+6, 6)*8^n.

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A162007 Third left hand column of the EG1 triangle A162005.

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A130812 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,...n).

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A172242 Number of 10-D hypercubes in an n-dimensional hypercube.

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A130811 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 5-subsets of X containing none of X_i, (i=1,...n).

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A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.

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A140405 a(n) = binomial(n+6, 6)*5^n.

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A119886 a(n) = 20a(n-2) - 64a(n-4).