A202153 G.f.: Sum_{n>=0} x^n * Product_{k=0..n-1} (1 + (2*k+1)*x).

1, 1, 2, 5, 13, 40, 127, 443, 1610, 6207, 24919, 104440, 453913, 2042537, 9488242, 45403797, 223433077, 1128619968, 5844484375, 30981783123, 167949231882, 929951967519, 5254958379951, 30276315741008, 177717403802001, 1061989593129105, 6456342053713346

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

Formula

G.f.: 1 + x*(1+x)/( G(0) - x*(1+x) ) where G(k) = 1 + x + x^2*(2*k+1)- x*(2*x*k+1+3*x)/G(k+1) ; G(0) = x*(1+x) if k->infinity; (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 04 2013

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 13*x^4 + 40*x^5 + 127*x^6 +...
where
A(x) = 1 + x*(1+x) + x^2*(1+x)*(1+3*x) + x^3*(1+x)*(1+3*x)*(1+5*x) +...

Prog

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

Crossrefs

Cf. A124380.

Sequence in context: A149863 A371714 A291614 * A149864 A149865 A174146

Adjacent sequences: A202150 A202151 A202152 * A202154 A202155 A202156

Keyword

nonn

Author

Paul D. Hanna, Dec 13 2011

Status

approved