OFFSET
0,3
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.
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]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
René Gy, May 10 2017
STATUS
approved