A135753 E.g.f.: A(x) = Sum_{n>=0} exp((3^n-1)/2*x)*x^n/n!.
1, 1, 3, 16, 153, 2536, 72513, 3571156, 303033153, 44411895376, 11247688063233, 4933176144494236, 3746180187749948193, 4933259445571307491096, 11257237602638666745470913, 44566655569041016108120599556
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..85
Programs
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Mathematica
Flatten[{1,Table[Sum[Binomial[n,k]*((3^k-1)/2)^(n-k),{k,0,n}],{n,1,20}]}] (* Vaclav Kotesovec, Jun 25 2013 *) -
PARI
a(n)=sum(k=0,n,binomial(n,k)*((3^k-1)/2)^(n-k))
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PARI
a(n)=n!*polcoeff(sum(k=0,n,exp((3^k-1)/2*x)*x^k/k!),n)
Formula
a(n) = Sum_{k=0..n} binomial(n,k)*[(3^k-1)/2]^(n-k).
a(n) ~ c * 3^(n^2/4)*2^((n+1)/2)/sqrt(Pi*n), where c = Sum_{k = -infinity..infinity} 2^k*3^(-k^2) = 1.8862156350800186... if n is even and c = Sum_{k = -infinity..infinity} 2^(k+1/2)*3^(-(k+1/2)^2) = 1.8865940733664341... if n is odd. - Vaclav Kotesovec, Jun 25 2013