A231172 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k - x) / (1 - k*x).

1, 1, 2, 9, 55, 412, 3665, 37809, 443998, 5848921, 85425959, 1370144160, 23941364521, 452710417321, 9210564625442, 200626664154849, 4658472162245695, 114865936425213532, 2997499707147860825, 82533717939413618649, 2391252655460083134718, 72723156542550310492081, 2316342951911550838935119

Offset

0,3

Comments

Compare to a g.f. of the Fibonacci numbers (A000045):

Sum_{n>=0} x^n * Product_{k=1..n} (k + x)/(1 + k*x) = 1/(1-x-x^2).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..420

Formula

a(n) = Sum_{k=0..n} A231171(n,k)*(-1)^k for n>=0.

Limit n->infinity (a(n)/n!)^(1/n) = 1/log(2). - Vaclav Kotesovec, May 09 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 55*x^4 + 412*x^5 + 3665*x^6 +...
where
A(x) = 1 + x*(1-x)/(1-x) + x^2*(1-x)*(2-x)/((1-x)*(1-2*x)) + x^3*(1-x)*(2-x)*(3-x)/((1-x)*(1-2*x)*(1-3*x)) + x^4*(1-x)*(2-x)*(3-x)*(4-x)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) +...

Prog

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

Crossrefs

Cf. A231171, A231173.

Sequence in context: A366177 A355281 A036074 * A009363 A069564 A109366

Adjacent sequences: A231169 A231170 A231171 * A231173 A231174 A231175

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2013

Status

approved