A009340 E.g.f. log(1 + sin(x)*exp(x)).

0, 1, 1, -2, -2, 20, -24, -352, 1968, 5840, -126944, 278848, 8284288, -76872640, -400462464, 12744251648, -38515617792, -1843130033920, 23434765820416, 182086013314048, -7427539628214272, 27218422422656000

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n)=2*sum(k=1..n, sum(j=0..(n-k)/2, binomial(n,n-k-2*j)*(k^(n-k-2*j)*sum(i=0..k/2, (2*i-k)^(k+2*j)*binomial(k,i)*(-1)^(j-i+1))))/(2^k*k)). - Vladimir Kruchinin, Jun 13 2011

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 0.840089206911... = abs(1/r), where r is the complex root of the equation r = log(-1/sin(r)). - Vaclav Kotesovec, Nov 03 2013

Mathematica

With[{nn=30}, CoefficientList[Series[Log[1+Sin[x]Exp[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, May 06 2013 *)

Prog

(Maxima)
a(n):=2*sum(sum(binomial(n, n-k-2*j)*(k^(n-k-2*j)*sum((2*i-k)^(k+2*j)*binomial(k, i)*(-1)^(j-i+1), i, 0, k/2)), j, 0, (n-k)/2)/(2^k*k), k, 1, n); /* Vladimir Kruchinin, Jun 13 2011 */

Crossrefs

Sequence in context: A370709 A103129 A322898 * A053593 A002907 A350466

Adjacent sequences: A009337 A009338 A009339 * A009341 A009342 A009343

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved