A216860 G.f.: Sum_{n>=0} n!^2 * x^n / Product_{k=1..n} (1 + k*x)^2.

1, 1, 2, 15, 232, 5693, 202398, 9829771, 624964724, 50365047225, 5016187555114, 604968014349767, 86878610741366976, 14648881145458377397, 2865572277481996560950, 643666405504709227632003, 164536267335939429654990988, 47489465018413227906492425009

Offset

0,3

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(-1) * (n!)^2. - Vaclav Kotesovec, Nov 02 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 232*x^4 + 5693*x^5 + 202398*x^6 +...
where
A(x) = 1 + x/(1+x)^2 + 2!^2*x^2/((1+x)*(1+2*x))^2 + 3!^2*x^3/((1+x)*(1+2*x)*(1+3*x))^2 + 4!^2*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^2 +...

Prog

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

Crossrefs

Cf. A216859.

Sequence in context: A197236 A097628 A305111 * A161968 A294043 A326095

Adjacent sequences: A216857 A216858 A216859 * A216861 A216862 A216863

Keyword

nonn

Author

Paul D. Hanna, Sep 17 2012

Status

approved