A191298 Expansion of exp(x*sin(x)) = 1 + Sum_{n>0} a(n)*x^(2*n)/(2*n-1)!.

1, 1, 2, 1, -99, -1079, 23495, 966525, -16291261, -1873014575, 27516674607, 7224252321637, -115719553200757, -50076660708857799, 1204475857461455111, 569715992136327120781, -24507410696611760644125, -9814015942898985962042975, 770782760061897531253976159, 237378562542668565550332844725

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n)=sum(k=1..n, binomial(2*n,k)*(sum(i=0..k/2, (2*i-k)^(2*n-k)*binomial(k,i)*(-1)^(n-i)))/(2^k))/n, n>0, a(0)=1.

Prog

(Maxima)
a(n):=sum(binomial(2*n, k)*(sum((2*i-k)^(2*n-k)*binomial(k, i)*(-1)^(n-i), i, 0, k/2))/(2^k), k, 1, n)/n;

Crossrefs

Sequence in context: A147805 A141527 A301631 * A104025 A335600 A039923

Adjacent sequences: A191295 A191296 A191297 * A191299 A191300 A191301

Keyword

sign

Author

Vladimir Kruchinin, May 30 2011

Status

approved