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 A286483 a(n) = (i^n)*Sum_{k=0..n} (k+1)*B_k*|s(n+2,k+2)|*(n+2)^k. 1
 1, 0, 5, 0, 238, 0, 51508, 0, 35028576, 0, 59053389408, 0, 209726098354368, 0, 1397532391623302400, 0, 16043549794523492290560, 0, 297285345537576037788672000, 0, 8447414796960536731803240038400 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A157302 A275759 A222327 * A264884 A036946 A027641 Adjacent sequences:  A286480 A286481 A286482 * A286484 A286485 A286486 KEYWORD nonn AUTHOR René Gy, May 10 2017 STATUS approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)