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A009257 E.g.f. exp(tanh(log(1+x))). 0


%S 1,1,0,-2,4,6,-74,190,1128,-14336,51616,404856,-7330520,41023048,

%T 250083744,-7532037344,65189204416,185746926720,-13324842809792,

%U 175157684686144,-215786634724224,-35458746254274944,711274631768613760

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

%F a(n)=sum(m=1..n, sum(r=0..n-m, stirling1(n,r+m)*sum(k=0..r, binomial(k+m-1,m-1)*(k+m)!*(-1)^(k)*2^(r-k)*stirling2(r+m,k+m)))/m!), n>0, a(0)=1. [From Vladimir Kruchinin, Jun 06 2011]

%t With[{nn=30},CoefficientList[Series[Exp[Tanh[Log[1+x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 15 2015 *)

%o (Maxima)

%o a(n):=sum(sum(stirling1(n,r+m)*sum(binomial(k+m-1,m-1)*(k+m)!*(-1)^(k)*2^(r-k)*stirling2(r+m,k+m),k,0,r),r,0,n-m)/m!,m,1,n); [From Vladimir Kruchinin, Jun 06 2011]

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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

%E Prior Mathematica program replaced by _Harvey P. Dale_, Jan 15 2015

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Last modified November 26 07:23 EST 2015. Contains 264487 sequences.