A216859 G.f.: Sum_{n>=0} n!^2 * x^n / Product_{k=1..2*n} (1 + k*x).

1, 1, 1, 3, 65, 1871, 69885, 3466339, 222981385, 18102473271, 1811907033269, 219290184518315, 31573338878091585, 5334099790769759551, 1045025926871985755053, 235016617680587793977331, 60133997212733124023350265, 17369999617568255471165082311

Offset

0,4

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..220

Formula

a(n) ~ exp(-2) * (n!)^2. - Vaclav Kotesovec, Nov 01 2014

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 65*x^4 + 1871*x^5 + 69885*x^6 +...
where
A(x) = 1 + x/((1+x)*(1+2*x)) + 2!^2*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) +
3!^2*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)) +
4!^2*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, m!^2*x^m/prod(k=1, 2*m, 1+k*x +x*O(x^n)) ), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A208885, A216860.

Sequence in context: A197043 A188984 A112000 * A346162 A012804 A348084

Adjacent sequences: A216856 A216857 A216858 * A216860 A216861 A216862

Keyword

nonn

Author

Paul D. Hanna, Sep 17 2012

Status

approved