A235776 E.g.f.: exp( Sum_{n>=1} x^(2*n) * Sum_{k=1..n} 1/k^2 ).

1, 2, 42, 2000, 170660, 22741992, 4344779208, 1123066676160, 376718037181200, 158895919895100960, 82222168141278271392, 51172838316787466103552, 37687233953299944682503744, 32399590493755848692815785600, 32140659218911596667452247171200

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Example

E.g.f.: A(x) = 1 + 2*x^2/2! + 42*x^4/4! + 2000*x^6/6! + 170660*x^8/8! +...
such that
log(A(x)) = x^2 + (1+1/4)*x^4 + (1+1/4+1/9)*x^6 + (1+1/4+1/9+1/16)*x^8 + (1+1/4+1/9+1/16+1/25)*x^10 + (1+1/4+1/9+1/16+1/25+1/36)*x^12 +...
Explicitly,
log(A(x)) = x^2 + 5/4*x^4 + 49/36*x^6 + 205/144*x^8 + 5269/3600*x^10 + 5369/3600*x^12 + 266681/176400*x^14 +...+ [Sum_{k=1..n} 1/k^2]*x^(2*n) +...

Prog

(PARI) {a(n)=local(A=1); A=exp(sum(m=1, n\2+1, sum(k=1, m, 1/k^2)*x^(2*m))+x*O(x^n)); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(2*n), ", "))

Crossrefs

Cf. A087761, A235385.

Sequence in context: A360238 A216029 A124103 * A216336 A152286 A293864

Adjacent sequences: A235773 A235774 A235775 * A235777 A235778 A235779

Keyword

nonn

Author

Paul D. Hanna, Jan 15 2014

Status

approved