A199746 E.g.f.: 1/(1 + Sum_{n>=1} (-1)^n*x^(n*(3*n-1)/2)/(n*(3*n-1)/2)! + (-1)^n*x^(n*(3*n+1)/2)/(n*(3*n+1)/2)! ).

1, 1, 3, 12, 66, 449, 3678, 35111, 383192, 4704300, 64172052, 962908056, 15762088585, 279514500434, 5338014558032, 109224066408835, 2383887010044728, 55281768382909480, 1357381019671809552, 35180557115610914376, 959798458208463538416, 27494554196938752676656

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) is odd iff n is a generalized pentagonal number (A001318).

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 12*x^3/3! + 66*x^4/4! + 449*x^5/5! + 3678*x^6/6! +...
where the reciprocal involves generalized pentagonal factorials:
A(x) = 1/(1 - x - x^2/2! + x^5/5! + x^7/7! - x^12/12! - x^15/15! + x^22/22! + x^26/26! - x^35/35! - x^40/40! +...).

Prog

(PARI) {a(n)=n!*polcoeff(1/(1+sum(m=1, n, (-1)^m*x^(m*(3*m-1)/2)/(m*(3*m-1)/2)!+(-1)^m*x^(m*(3*m+1)/2)/(m*(3*m+1)/2)! +x*O(x^n))), n)}

Crossrefs

Cf. A001318.

Sequence in context: A214565 A267323 A058790 * A293302 A248871 A080599

Adjacent sequences: A199743 A199744 A199745 * A199747 A199748 A199749

Keyword

nonn

Author

Paul D. Hanna, Nov 09 2011

Status

approved