A189919 O.g.f.: Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 - (2*k-1)*x).

1, 1, 3, 15, 105, 933, 10023, 126195, 1821165, 29625513, 536223723, 10687190775, 232544252625, 5484912970893, 139387510991823, 3796699051667355, 110344769466766485, 3408297041928101073, 111490951250101642323, 3850360096498676899935

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Formula

a(n) ~ 2^(n+1) * n! / (3^(3/2) * (log(3))^(n+1)). - Vaclav Kotesovec, Nov 01 2014

Example

G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 105*x^4 + 933*x^5 + 10023*x^6 +...
where
A(x) = 1 + x/(1-x) + 2!*x^2/((1-x)*(1-3*x)) + 3!*x^3/((1-x)*(1-3*x)*(1-5*x)) + 4!*x^4/((1-x)*(1-3*x)*(1-5*x)*(1-7*x)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, m!*x^m/prod(k=1, m, 1-(2*k-1)*x+x*O(x^n))), n)}

Crossrefs

Sequence in context: A357596 A249014 A258498 * A360579 A251598 A338725

Adjacent sequences: A189916 A189917 A189918 * A189920 A189921 A189922

Keyword

nonn

Author

Paul D. Hanna, Jul 22 2011

Status

approved