A193110 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1+k*x)/(1-k*x).

1, 1, 3, 9, 33, 137, 635, 3233, 17881, 106489, 678091, 4590225, 32873625, 248056497, 1965232403, 16297012121, 141080069057, 1271902272241, 11916559511731, 115805756278393, 1165319447579313, 12123219789825273, 130206136096941195

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..370

Formula

G.f.: 1 + x*(1 - G(0) )/(1-x) where G(k) = 1 - (1+x*(k+1))/(1-x*(k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 18 2013

Example

G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 33*x^4 + 137*x^5 + 635*x^6 +...
where
A(x) = 1 + x*(1+x)/(1-x) + x^2*(1+x)*(1+2*x)/((1-x)*(1-2*x)) + x^3*(1+x)*(1+2*x)*(1+3*x)/((1-x)*(1-2*x)*(1-3*x)) +...

Prog

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

Crossrefs

Sequence in context: A207542 A009212 A153344 * A001930 A049425 A333889

Adjacent sequences: A193107 A193108 A193109 * A193111 A193112 A193113

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2011

Status

approved