A305711 Expansion of e.g.f. exp(2*x/(exp(x) + 1)).

1, 1, 0, -2, -1, 11, 13, -111, -220, 1756, 5051, -39775, -153191, 1215345, 5952668, -48020714, -288569149, 2377190003, 17069110381, -143857868895, -1209439895944, 10435153277620, 101078662547567, -892827447251575, -9834570608359487, 88900938146195601, 1101567283699652888

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Wikipedia, Genocchi number

Index entries for sequences related to Bernoulli numbers

Example

exp(2*x/(exp(x) + 1)) = 1 + x - 2*x^3/3! - x^4/4! + 11*x^5/5! + 13*x^6/6! - 111*x^7/7! - 220*x^8/8! + ...

Maple

a:=series(exp(2*x/(exp(x)+1)), x=0, 27): seq(n!*coeff(a, x, n), n=0..26); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 26; CoefficientList[Series[Exp[2 x/(Exp[x] + 1)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[k EulerE[k - 1, 0] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 26}]
a[n_] := a[n] = Sum[2 (1 - 2^k) BernoulliB[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A036968, A296835, A296836.

Sequence in context: A140316 A295852 A088587 * A158352 A158354 A055459

Adjacent sequences: A305708 A305709 A305710 * A305712 A305713 A305714

Keyword

sign

Author

Ilya Gutkovskiy, Jun 08 2018

Status

approved