A383155 a(n) = Sum_{k=0..n} k^6 * (-1)^k * 3^(n-k) * binomial(n,k).

0, -1, 58, -180, -1304, -2920, 1008, 34496, 163840, 525312, 1285120, 2241536, 1124352, -12113920, -72052736, -282378240, -924581888, -2699493376, -7201751040, -17666670592, -39507722240, -77918109696, -121883328512, -78622228480, 453588811776, 2904974950400, 11885785120768

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, A383152.

Programs

Magma

[&+[k^6 * (-1)^k * 3^(n-k) * Binomial(n,k): k in [0..n]]: n in [0..29]]; // Vincenzo Librandi, Apr 23 2025

Mathematica

Table[Sum[(k^6*(-1)^k*3^(n-k))*Binomial[n,k],{k,0,n}],{n,0,30}] (* Vincenzo Librandi, Apr 23 2025 *)

PARI

a(n) = 2^(n-6)*(-4368*n+7290*n^2-3555*n^3+645*n^4-45*n^5+n^6);

Formula

a(n) = 2^(n-6) * (-4368*n + 7290*n^2 - 3555*n^3 + 645*n^4 - 45*n^5 + n^6).