A216354 G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^n*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.

1, 2, 52, 58640, 3583098592, 11584364000042912, 2042518153012624794424576, 20047892010468651075834167466942080, 11138509206681372983092694151616405935206616064, 354938139483847646086359348765071470756626699510545192807936

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Example

G.f.: A(x) = 1 + 2*x + 52*x^2 + 58640*x^3 + 3583098592*x^4 +...
where
log(A(x)) = 2*x + 10^2*x^2/2 + 56^3*x^3/3 + 346^4*x^4/4 + 2252^5*x^5/5 + 15184^6*x^6/6 + 104960^7*x^7/7 +...+ A000172(n)^n*x^n/n +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3)^m*x^m/m+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A216355, A166990, A216352, A216353, A000172.

Sequence in context: A080973 A230882 A369089 * A079179 A000654 A061306

Adjacent sequences: A216351 A216352 A216353 * A216355 A216356 A216357

Keyword

nonn

Author

Paul D. Hanna, Sep 04 2012

Status

approved