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A383150

a(n) = Sum_{k=0..n} k^3 * (-1)^k * 3^(n-k) * binomial(n,k).

0, -1, 2, 18, 64, 160, 288, 224, -1024, -6912, -28160, -95744, -294912, -851968, -2351104, -6266880, -16252928, -41222144, -102629376, -251527168, -608174080, -1453326336, -3437232128, -8055160832, -18723373056, -43201331200, -99019128832, -225586446336

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

FORMULA

a(n) = 2^(n-3) * (-12*n + 9*n^2 - n^3).

G.f.: -x*(1 - 10*x + 22*x^2)/(1 - 2*x)^4. - Andrew Howroyd, Nov 13 2025

MATHEMATICA

Table[2^(n-3)*(-12*n+9*n^2-n^3), {n, 0, 30}] (* Vincenzo Librandi, May 02 2025 *)

PROG