A009282 - OEIS

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A009282

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

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