A009283 -id:A009283 - cp's OEIS frontend

A330046 Expansion of e.g.f. exp(x) / (1 - sinh(x)).

1, 2, 5, 17, 77, 437, 2975, 23627, 214457, 2189897, 24846395, 310095887, 4221990437, 62273111357, 989164604615, 16834483468547, 305604501324017, 5894522593612817, 120381876933435635, 2595103478745235607, 58887707028270711197, 1403084759749993342277

Offset: 0

Ilya Gutkovskiy, Nov 28 2019

nonn

Binomial transform of A006154.

Cf. A000629, A006154, A009283, A327034, A330047.

nmax = 21; CoefficientList[Series[Exp[x]/(1 - Sinh[x]), {x, 0, nmax}], x] Range[0, nmax]!

a(n) = Sum_{k=0..n} binomial(n,k) * A006154(k).

a(n) ~ n! * (1 + 1/sqrt(2)) / (log(1 + sqrt(2)))^(n+1). - Vaclav Kotesovec, Dec 03 2019

A009282 Expansion of e.g.f.: exp(x + sin(x)).

Original entry on oeis.org

1, 2, 4, 7, 8, -7, -74, -209, -40, 2441, 10954, 6667, -185524, -1041739, -510530, 26716831, 158378768, -47260303, -6226501934, -34323431789, 71521515284, 2087815263725, 9437342779558, -55046954388953, -923175950185960, -2736047549718871, 43387645616657338

Offset: 0

R. H. Hardin

Cf. A002017, A009209, A009283.

With[{nn=30},CoefficientList[Series[Exp[x+Sin[x]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 23 2014 *)

x='x+O('x^66); Vec(serlaplace(exp(x + sin(x)))) /* Joerg Arndt, Sep 01 2012 */

E.g.f.: exp(x + sin(x)).

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 10 2022

Extended with signs by Olivier Gérard, Mar 15 1997

Name corrected by Arkadiusz Wesolowski, Sep 01 2012

cp's OEIS Frontend

A330046 Expansion of e.g.f. exp(x) / (1 - sinh(x)).

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