A383152 a(n) = Sum_{k=0..n} k^5 * (-1)^k * 3^(n-k) * binomial(n,k).

0, -1, 26, 18, -272, -1400, -4032, -7168, -1024, 55296, 294400, 1086976, 3354624, 9132032, 22249472, 47923200, 85983232, 99155968, -102629376, -1237712896, -5688524800, -20775960576, -67868033024, -207022456832, -602167836672, -1690304512000, -4613767954432

Offset: 0

Author

Seiichi Manyama, Apr 18 2025

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A001787, A178987, A383150, A383151, A383155.

Programs

Magma

[&+[k^5 * (-1)^k * 3^(n-k) * Binomial(n, k): k in [0..n]]: n in [0..29]]; // Vincenzo Librandi, Apr 23 2025

Mathematica

Table[2^(n-5)*(-480*n+690*n^2-255*n^3+30*n^4-n^5),{n,0,50}] (* Vincenzo Librandi, Apr 24 2025 *)

PARI

a(n) = 2^(n-5)*(-480*n+690*n^2-255*n^3+30*n^4-n^5);

Formula

a(n) = 2^(n-5) * (-480*n + 690*n^2 - 255*n^3 + 30*n^4 - n^5).