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A009212 E.g.f. exp(sin(x)*exp(x)). 0

%I

%S 1,1,3,9,33,137,619,3017,15617,84625,474771,2723721,15730209,89487257,

%T 482793211,2259370697,6292321025,-41172399839,-1066104760797,

%U -14517156416247,-163539106749663,-1652237279663959,-15169567281615221

%N E.g.f. exp(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)^(k+j-i))))/(2^k*k!)), n>0, a(0)=1. [From Vladimir Kruchinin, Jun 13 2011]

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

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

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs Mar 15 1997 by _Olivier GĂ©rard_.

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Last modified July 22 21:23 EDT 2014. Contains 244844 sequences.