A205802 Expansion of e.g.f. 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

1, 1, 2, 6, 23, 110, 630, 4200, 31990, 274051, 2608220, 27304530, 311820630, 3857738170, 51397726380, 733698365400, 11171708347799, 180738402744866, 3096027531044102, 55980949167688884, 1065496642477438890, 21293801805033731190, 445818117237227995260

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..400

Formula

E.g.f.: 1/( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 6*x^3/3! + 23*x^4/4! + 110*x^5/5! + ...
where
1/A(x) = 1 - x + x^4/4! - x^9/9! + x^16/16! - x^25/25! + x^36/36! + ...

Prog

(PARI) {a(n)=n!*polcoeff(sum(m=0, sqrtint(n+1), (-1)^m*x^(m^2)/(m^2)!+x*O(x^n))^(-1), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A198891, A205800, A205801.

Sequence in context: A264899 A224786 A320566 * A117226 A117156 A201692

Adjacent sequences: A205799 A205800 A205801 * A205803 A205804 A205805

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2012

Status

approved