A193318 G.f.: Sum_{n>=0} x^n*Product_{k=1..n} (1 - (2*k-1)*x) / (1 - (2*k)*x).

1, 1, 2, 5, 15, 54, 229, 1111, 6020, 35873, 232677, 1629528, 12238621, 98006533, 832764146, 7477375601, 70696248123, 701636328534, 7289525389681, 79084544097475, 893993204314316, 10509131215500701, 128235999632164377, 1621637635101089040

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..210

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 54*x^5 + 229*x^6 +...
where
A(x) =  1 + x*(1-x)/(1-2*x) + x^2*(1-x)*(1-3*x)/((1-2*x)*(1-4*x)) + x^3*(1-x)*(1-3*x)*(1-5*x)/((1-2*x)*(1-4*x)*(1-6*x)) +...

Prog

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

Crossrefs

Sequence in context: A208237 A321958 A107112 * A171450 A204190 A051295

Adjacent sequences: A193315 A193316 A193317 * A193319 A193320 A193321

Keyword

nonn

Author

Paul D. Hanna, Jul 22 2011

Status

approved