A208885 G.f.: Sum_{n>=0} (2*n)! * x^n / Product_{k=1..2*n} (1 + k*x).

1, 2, 18, 494, 26730, 2360462, 307793178, 55540518014, 13245448695210, 4033344237266222, 1526730007443860538, 703123406641373962334, 387107509435656840975690, 251064026710334080621248782, 189445984864409630341273915098, 164548892048219588850960940699454

Offset

0,2

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n! * x^n/Product_{k=1..n} (1+k*x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ sqrt(Pi) * 2^(2*n+1) * n^(2*n+1/2) / exp(2*n+1/2). - Vaclav Kotesovec, Nov 01 2014

Example

G.f.: A(x) = 1 + 2*x + 18*x^2 + 494*x^3 + 26730*x^4 + 2360462*x^5 +...
such that
A(x) = 1 + 2!*x/((1+x)*(1+2*x)) + 4!*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) + 6!*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)) + 8!*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)*(1+8*x)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, (2*m)!*x^m/prod(k=1, 2*m, 1+k*x+x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A208886, A216859.

Sequence in context: A355134 A277037 A015203 * A255433 A121936 A380274

Adjacent sequences: A208882 A208883 A208884 * A208886 A208887 A208888

Keyword

nonn

Author

Paul D. Hanna, Mar 04 2012

Status

approved