A184359 Recurrence: Sum_{n>=0} a(n-k)*a(k) = (n+1)!^2/2^n.

1, 1, 4, 32, 410, 7562, 188736, 6118296, 249991926, 12575954918, 764125698224, 55189878377480, 4674557178309388, 458942541226822876, 51705551381013381112, 6626012145599584408536, 958371653002293850802814

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

Self-convolution equals A184358.

G.f. satisfies: A(x) = F(x*A(x)^2) where A(x/F(x)^2) = F(x) is the g.f. of A184361.

G.f.: A(x) = sqrt((1/x)*Series_Reversion(x/F(x)^2)) where F(x) is the g.f. of A184361.

Example

 G.f.: A(x) = 1 + x + 4*x^2 + 32*x^3 + 410*x^4 + 7562*x^5 +...
A(x)^2 = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 + 396900*x^6 +...+ (n+1)!^2*x^n/2^n +...
The g.f. of A184361 is F(x) = A(x/F(x)^2):
F(x) = 1 + x + 2*x^2 + 15*x^3 + 204*x^4 + 4085*x^5 + 110128*x^6 +...

Prog

 (PARI) {a(n)=local(G=sum(m=0, n, (m+1)!^2*x^m/2^m)+x*O(x^n)); polcoeff(sqrt(G), n)}

Crossrefs

Cf. A184358, A184360, A184361.

Sequence in context: A317677 A365603 A191459 * A350465 A229548 A005172

Adjacent sequences: A184356 A184357 A184358 * A184360 A184361 A184362

Keyword

nonn

Author

Paul D. Hanna, Jan 16 2011

Status

approved