A074707 exp(Sum_{n>0} x^n/n^2) = Sum_{n>=0} a(n)*x^n/n!^2.

1, 1, 3, 19, 214, 3846, 102206, 3795758, 188648664, 12125977944, 980768153832, 97599402813672, 11728820086206576, 1675575398007779568, 280777781273956353648, 54556438705747006028016, 12169284368165386948212096, 3088938134820388829982311808

Offset

0,3

References

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, second edition, Addison Wesley, pp. 464-466.

Links

Table of n, a(n) for n=0..17.

Formula

a(n)=n!^2/n*sum(k=0, n-1, a(k)/k!^2/(n-k)). a(n)/n!^2 = exp(Pi^2/6)/n^2 + O(log(n)/n^3). - Benoit Cloitre, Jan 11 2003

Prog

(PARI) a(n)=if(n<2, 1, (n-1)!^2+n!^2/n*sum(k=1, n-1, a(k)/k!^2/(n-k)))
(PARI) {a(n)=n!^2*polcoeff(exp(sum(m=1, n, x^m/m^2)+x*O(x^n)), n)}

Crossrefs

Cf. A193436, A217145.

Sequence in context: A165356 A000275 A058165 * A230317 A135749 A005647

Adjacent sequences: A074704 A074705 A074706 * A074708 A074709 A074710

Keyword

nonn

Author

Vladeta Jovovic, Sep 04 2002

Status

approved