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A225601
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a(n) = A000172(n)^n, where A000172(n) = Sum_{k=0..n} binomial(n,k)^3 forms the Franel numbers.
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0
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1, 2, 100, 175616, 14331920656, 57921784155180032, 12255108779062338588246016, 140335244044685299494850396160000000, 89108073653130217591789722357691598453905367296, 3194443255354428321611505213481524389463527731906791539474432
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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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L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} A216354(n)*x^n ).
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EXAMPLE
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L.g.f.: L(x) = 2*x + 100*x^2/2 + 175616*x^3/3 + 14331920656*x^4/4 + 57921784155180032*x^5/5 +...
where exponentiation is an integer series:
exp(L(x)) = 1 + 2*x + 52*x^2 + 58640*x^3 + 3583098592*x^4 + 11584364000042912*x^5 +...+ A216354(n)*x^n +...
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PROG
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)^3)^n}
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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