A362994 a(n) = lcm(1, 2, ..., n+1) * Bernoulli(n, 1). Alternating row sums of A362995 and A363154.

1, 1, 1, 0, -2, 0, 10, 0, -84, 0, 2100, 0, -91212, 0, 420420, 0, -86894808, 0, 12796881240, 0, -123176186952, 0, 33154044803880, 0, -2317852458291480, 0, 114488177740536600, 0, -63580025062953158760, 0, 43435207772044760997000, 0, -2182849703429651931795120

Offset: 0

Author

Peter Luschny, May 14 2023

Keywords

• sign

Links

• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Cf. A362995 (alternating row sum), A363154 (alternating row sum), A003418 (lcm), A164555/A027642 (Bernoulli), A362991 (column 0).

Programs

Maple

A362994 := n -> ilcm(seq(i + 1, i = 0..n)) * bernoulli(n, 1):
seq(A362994(n), n = 0..32);

Mathematica

A362994[n_]:=LCM@@Range[n+1]BernoulliB[n, 1];Array[A362994,50,0] (* Paolo Xausa, Aug 09 2023 *)

PARI

a(n) = lcm([1..n+1])*subst(bernpol(n), 'x, 1); \\ Michel Marcus, Aug 09 2023

Formula

a(n) = LCM(n) * Sum_{j=0..n} (-1)^(n - j) * j! * Stirling2(n, j) / (j + 1), where LCM(n) = lcm(i + 1, i = 0..n).