A056468 a(n) = Sum_{k=1..n} k^6*binomial(n,k).
0, 1, 66, 924, 7400, 44040, 217392, 942592, 3714048, 13593600, 46914560, 154328064, 487778304, 1490384896, 4423372800, 12801146880, 36235378688, 100580917248, 274361352192, 736775372800, 1950815354880, 5099601002496, 13176144920576, 33682341494784
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (14,-84,280,-560,672,-448,128).
Programs
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Mathematica
Table[Sum[k^6*Binomial[n, k], {k, n}], {n, 0, 30}] (* T. D. Noe, Nov 22 2013 *) -
PARI
a(n) = sum(k = 1, n, k^6*binomial(n,k)); \\ Michel Marcus, Nov 20 2013
Formula
a(n) = 2^(n-6)*n*(n+1)*(n^4 + 14*n^3 + 31*n^2 - 46*n + 16).
G.f.: -x*(136*x^4-272*x^3+84*x^2+52*x+1)/(2*x-1)^7. [Colin Barker, Sep 20 2012]