A286483 a(n) = (i^n)*Sum_{k=0..n} (k+1)*B_k*|s(n+2,k+2)|*(n+2)^k.

1, 0, 5, 0, 238, 0, 51508, 0, 35028576, 0, 59053389408, 0, 209726098354368, 0, 1397532391623302400, 0, 16043549794523492290560, 0, 297285345537576037788672000, 0, 8447414796960536731803240038400

Offset: 0

Author

René Gy, May 10 2017

Keywords

• nonn

Comments

|s(n,k)| is the unsigned Stirling number of first kind (see A008275), B_k is the Bernoulli number and i^2=-1. All even-indexed terms are positive integers, and the odd-indexed terms are zero. A generating function would be welcomed.

Links

• R. Gy, An aerated triangular array of integers, arXiv: 1902.09309 [math.CO], 2019.

Programs

Mathematica

list = {};
nlim = 20; Do[s=(-1)^(n/2) Sum[(-1)^(n-k)*(k+1)*BernoulliB[k]*StirlingS1[n+2,k+2]*(n+2)^k,{k,0,n}];AppendTo[list,s], {n,0,nlim}]; Print[list]

PARI

a(n) = (I^n)*sum(k=0, n, (k+1)*bernfrac(k)*abs(stirling(n+2,k+2,1))*(n+2)^k); \\ Michel Marcus, May 19 2019