A009212 E.g.f. exp(sin(x)*exp(x)).

1, 1, 3, 9, 33, 137, 619, 3017, 15617, 84625, 474771, 2723721, 15730209, 89487257, 482793211, 2259370697, 6292321025, -41172399839, -1066104760797, -14517156416247, -163539106749663, -1652237279663959, -15169567281615221

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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

Mathematica

Array[ SeriesCoefficient[ Series[ Exp[ Sin[ x ]*Exp[ x ] ], {x, 0, 30} ], # ]*#!&, 29, 0 ]

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)^(k+j-i), i, 0, k/2)), j, 0, (n-k)/2)/(2^k*k!), k, 1, n); /* Vladimir Kruchinin, Jun 13 2011 */

Crossrefs

Sequence in context: A320186 A320187 A207542 * A153344 A193110 A001930

Adjacent sequences: A009209 A009210 A009211 * A009213 A009214 A009215

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved