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A225601 a(n) = A000172(n)^n, where A000172(n) = Sum_{k=0..n} binomial(n,k)^3 forms the Franel numbers. 0

%I #8 Aug 03 2013 13:31:36

%S 1,2,100,175616,14331920656,57921784155180032,

%T 12255108779062338588246016,140335244044685299494850396160000000,

%U 89108073653130217591789722357691598453905367296,3194443255354428321611505213481524389463527731906791539474432

%N a(n) = A000172(n)^n, where A000172(n) = Sum_{k=0..n} binomial(n,k)^3 forms the Franel numbers.

%F L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} A216354(n)*x^n ).

%e L.g.f.: L(x) = 2*x + 100*x^2/2 + 175616*x^3/3 + 14331920656*x^4/4 + 57921784155180032*x^5/5 +...

%e where exponentiation is an integer series:

%e exp(L(x)) = 1 + 2*x + 52*x^2 + 58640*x^3 + 3583098592*x^4 + 11584364000042912*x^5 +...+ A216354(n)*x^n +...

%o (PARI) {a(n)=sum(k=0,n, binomial(n, k)^3)^n}

%o for(n=0,20,print1(a(n),", "))

%Y cf. A216354, A000172.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 03 2013

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)