A184361 Self-convolution equals A184360.

1, 1, 2, 15, 204, 4085, 110128, 3809974, 164121912, 8615474691, 541908913830, 40272139958565, 3493551786163290, 350048185790908410, 40136947555438179728, 5223165612267081234916, 765782709626083599128656

Offset: 0

Author

Paul D. Hanna, Jan 16 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 204*x^4 + 4085*x^5 +...
A(x)^2 = 1 + 2*x + 5*x^2 + 34*x^3 + 442*x^4 + 8638*x^5 + 229467*x^6 +...+ A184360(n)*x^n +...
		

Crossrefs

Cf. A184358, A184359, A184360.

Programs

PARI

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

Formula

G.f. satisfies: A(x) = G(x/A(x)^2) and A(x*G(x)^2) = G(x) is the g.f. of A184359.

G.f.: A(x) = sqrt(x/Series_Reversion(x*F(x))) where F(x) = Sum_{n>=0} (n+1)!^2*(x/2)^n is the g.f. of A184358.

G.f. satisfies: [x^n] A(x)^(2n+2)/(n+1) = (n+1)!^2/2^n = A184358(n).