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%I #20 Nov 26 2021 10:39:23
%S 0,1,66,924,7400,44040,217392,942592,3714048,13593600,46914560,
%T 154328064,487778304,1490384896,4423372800,12801146880,36235378688,
%U 100580917248,274361352192,736775372800,1950815354880,5099601002496,13176144920576,33682341494784
%N a(n) = Sum_{k=1..n} k^6*binomial(n,k).
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (14,-84,280,-560,672,-448,128).
%F a(n) = 2^(n-6)*n*(n+1)*(n^4 + 14*n^3 + 31*n^2 - 46*n + 16).
%F G.f.: -x*(136*x^4-272*x^3+84*x^2+52*x+1)/(2*x-1)^7. [_Colin Barker_, Sep 20 2012]
%t Table[Sum[k^6*Binomial[n, k], {k, n}], {n, 0, 30}] (* _T. D. Noe_, Nov 22 2013 *)
%o (PARI) a(n) = sum(k = 1, n, k^6*binomial(n,k)); \\ _Michel Marcus_, Nov 20 2013
%Y Cf. A001788, A059338, A058649, A058645.
%K nonn,easy
%O 0,3
%A _Benoit Cloitre_, Dec 06 2002
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