A231277 G.f.: sqrt( Sum_{n>=0} x^n * Product_{k=1..n} (2*k - x) / (1 - 2*k*x) ).

1, 1, 5, 43, 503, 7395, 130417, 2677347, 62652163, 1645424927, 47918249503, 1532532861117, 53400906126039, 2013774998655263, 81717093507007097, 3550624402561500703, 164477470918884953215, 8092070874197301949727, 421396510870277400155719

Offset

0,3

Comments

Limit n->infinity A231229(n) / A231277(n) = 2. - Vaclav Kotesovec, Nov 02 2014

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..235

Formula

Self-convolution yields A231229.

a(n) ~ 2^(n-2) * n! / (log(2))^(n+1). - Vaclav Kotesovec, Nov 02 2014

Example

A(x) = 1 + x + 5*x^2 + 43*x^3 + 503*x^4 + 7395*x^5 + 130417*x^6 +...
where
A(x)^2 = 1 + x*(2-x)/(1-2*x) + x^2*(2-x)*(4-x)/((1-2*x)*(1-4*x)) + x^3*(2-x)*(4-x)*(6-x)/((1-2*x)*(1-4*x)*(1-6*x)) + x^4*(2-x)*(4-x)*(6-x)*(8-x)/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)) +...

Prog

(PARI) {a(n)=polcoeff(sqrt(sum(m=0, n, x^m*prod(k=1, m, (2*k-x)/(1-2*k*x +x*O(x^n))))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A231229.

Sequence in context: A191802 A092471 A093620 * A188365 A107720 A362188

Adjacent sequences: A231274 A231275 A231276 * A231278 A231279 A231280

Keyword

nonn

Author

Paul D. Hanna, Nov 06 2013

Status

approved