A009340 - OEIS

%I #19 Apr 01 2017 14:04:00

%S 0,1,1,-2,-2,20,-24,-352,1968,5840,-126944,278848,8284288,-76872640,

%T -400462464,12744251648,-38515617792,-1843130033920,23434765820416,

%U 182086013314048,-7427539628214272,27218422422656000

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

%F 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

%F 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

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

%o (Maxima)

%o 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 */

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997