A009209 -id:A009209 - cp's OEIS frontend

A009227 Expansion of e.g.f.: exp(sinh(x))/exp(x).

1, 0, 0, 1, 0, 1, 10, 1, 56, 281, 246, 4621, 16412, 53197, 564642, 1937937, 13309648, 100397649, 454215214, 4082253589, 26498068420, 174791970677, 1575851086778, 10628056916313, 91523101970104, 788580099169337, 6237722665351750, 60190551618214941

Offset: 0

R. H. Hardin

Number of partitions of n-set in which block sizes are odd and greater than 1. - Vladeta Jovovic, Aug 23 2007

Cf. A003724, A009209.

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, 2*j)*a(n-2*j-1), j=1..(n-1)/2))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 09 2022

With[{nn=30},CoefficientList[Series[Exp[Sinh[x]]/Exp[x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 18 2015 *)

my(x='x+O('x^30)); Vec(serlaplace(exp(sinh(x))/exp(x))) \\ Michel Marcus, Apr 09 2022

a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 09 2022

Extended and signs tested by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Jan 18 2015

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

A009227 Expansion of e.g.f.: exp(sinh(x))/exp(x).

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