A363154 -id:A363154 - cp's OEIS frontend

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

Peter Luschny, May 14 2023

sign

Index entries for sequences related to Bernoulli numbers.

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

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

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

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

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).

A362990 Row sums of A363154.

Original entry on oeis.org

1, 1, 3, 8, 70, 156, 2982, 19296, 216396, 917480, 47847580, 250815120, 18724750980, 116905717320, 788402337660, 11422960203648, 1503958432951464, 12400297557081840, 2060467159019459400, 19050402239258292000, 185663459342909159640, 1902329957427442126320

Offset: 0

Peter Luschny, May 22 2023

nonn

Cf. A363154, A173018, A349203.

A362990 := n -> add(ilcm(seq(binomial(n, j), j = 0..n)) * combinat[eulerian1](n, k) / binomial(n, k), k = 0.. n): seq(A362990(n), n = 0..21);

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI