A229285 G.f.: Sum_{n>=0} x^n / Product_{k=1..2*n-1} (1 - k*x).

1, 1, 2, 8, 42, 260, 1860, 15020, 134336, 1313696, 13911528, 158279872, 1922455440, 24794405328, 338037825952, 4853075024192, 73123573392416, 1152965052858560, 18974557508679104, 325181733420301504, 5791431588096653824, 106990656473333558528, 2046805540661737323136

Offset

0,3

Comments

Compare to o.g.f. of Bell numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

Example

G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 42*x^4 + 260*x^5 + 1860*x^6 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)*(1-3*x)) + x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)) +...

Prog

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

Crossrefs

Cf. A229286.

Sequence in context: A130649 A054993 A188912 * A339460 A005315 A182520

Adjacent sequences: A229282 A229283 A229284 * A229286 A229287 A229288

Keyword

nonn

Author

Paul D. Hanna, Sep 18 2013

Status

approved