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

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

Mathematica

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

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 */

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997