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

0,3

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (14,-84,280,-560,672,-448,128).

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

a(n) = 14*a(n-1) - 84*a(n-2) + 280*a(n-3) - 560*a(n-4) + 672*a(n-5) - 448*a(n-6) + 128*a(n-7). - Wesley Ivan Hurt, Jun 05 2026

Mathematica

Table[Sum[k^6*Binomial[n, k], {k, n}], {n, 0, 30}] (* T. D. Noe, Nov 22 2013 *)

Prog

(PARI) a(n) = sum(k = 1, n, k^6*binomial(n, k)); \\ Michel Marcus, Nov 20 2013

Crossrefs

Cf. A001788, A059338, A058649, A058645.

Sequence in context: A293613 A304838 A337896 * A027785 A271757 A228996

Adjacent sequences: A056465 A056466 A056467 * A056469 A056470 A056471

Keyword

nonn,easy,changed

Author

Benoit Cloitre, Dec 06 2002

Status

approved