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A235776 E.g.f.: exp( Sum_{n>=1} x^(2*n) * Sum_{k=1..n} 1/k^2 ). 0
1, 2, 42, 2000, 170660, 22741992, 4344779208, 1123066676160, 376718037181200, 158895919895100960, 82222168141278271392, 51172838316787466103552, 37687233953299944682503744, 32399590493755848692815785600, 32140659218911596667452247171200 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A360238 A216029 A124103 * A216336 A152286 A293864
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2014
STATUS
approved

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Last modified March 2 05:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)