A249636 G.f.: Sum_{n>=0} x^n / Product_{k=n..2*n-1} (1 - k*x).

1, 1, 2, 7, 33, 186, 1213, 8949, 73300, 657589, 6396829, 66936872, 748528619, 8896663389, 111873459298, 1482522176651, 20633389026901, 300705290677218, 4576892504775417, 72584518271451169, 1196883163316172252, 20482129284796798609, 363138667441109774065, 6659922487212111452776

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 33*x^4 + 186*x^5 + 1213*x^6 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-2*x)*(1-3*x)) + x^3/((1-3*x)*(1-4*x)*(1-5*x)) + x^4/((1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)) + x^5/((1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) +...

Prog

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

Crossrefs

Sequence in context: A086618 A224769 A302285 * A172387 A186760 A162661

Adjacent sequences: A249633 A249634 A249635 * A249637 A249638 A249639

Keyword

nonn

Author

Paul D. Hanna, Nov 02 2014

Status

approved