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A126152
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Main diagonal of symmetric triangle A126150: a(n) = A126150(n,n).
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5
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1, 4, 36, 744, 28536, 1736064, 152914176, 18372559104, 2885671339776, 573765893121024, 140835811776316416, 41820352964911908864, 14774712204104658671616, 6124078747943873540112384
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/(1 - 4*x/(1-5*x/(1 - 21*x/(1-22*x/(1 - 50*x/(1-51*x/(1 - 91*x/(1-92*x/(1 -...)))))))))))), a continued fraction involving even-indexed pentagonal numbers A000326. - Paul D. Hanna, Feb 15 2012
a(n) ~ Gamma(1/3) * 2^(3*n+7/3) * 3^(n+3/2) * n^(2*n+7/6) / (exp(2*n) * Pi^(2*n+13/6)). - Vaclav Kotesovec, May 30 2015
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PROG
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(PARI) /* Continued fraction involving even-indexed pentagonal numbers: */
{a(n)=local(CF=1+x*O(x), m, P); for(k=1, n, m=2*((n-k)\2+1); P=m*(3*m-1)/2-((n-k+1)%2); CF=1/(1-P*x*CF)); polcoeff(CF, n, x)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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