A383151 a(n) = Sum_{k=0..n} k^4 * (-1)^k * 3^(n-k) * binomial(n,k).

0, -1, 10, 36, 40, -160, -1152, -4480, -13568, -34560, -74240, -123904, -92160, 425984, 2867200, 11796480, 40763392, 128122880, 378667008, 1070858240, 2928148480, 7795113984, 20300431360, 51900317696, 130610626560, 324219699200, 795206483968, 1929715384320

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Formula

a(n) = 2^(n-4) * (-66*n + 75*n^2 - 18*n^3 + n^4).

G.f.: -x*(1 - 4*x)*(1 - 16*x + 40*x^2)/(1 - 2*x)^5. - Andrew Howroyd, Nov 13 2025

Mathematica

Table[Sum[(k^4*(-1)^k*3^(n-k))*Binomial[n, k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Apr 23 2025 *)

Prog

(PARI) a(n) = 2^(n-4)*(-66*n+75*n^2-18*n^3+n^4);
(Magma) [&+[k^4 * (-1)^k * 3^(n-k) * Binomial(n, k): k in [0..n]]: n in [0..29]]; // Vincenzo Librandi, Apr 23 2025

Crossrefs

Cf. A001787, A178987, A383150, A383152, A383155.

Sequence in context: A125550 A343155 A223305 * A176575 A073613 A346386

Adjacent sequences: A383148 A383149 A383150 * A383152 A383153 A383154

Keyword

sign,easy

Author

Seiichi Manyama, Apr 18 2025

Status

approved