A246573 G.f.: sqrt( Sum_{n>=0} x^n / (1-x)^(4*n+3) * [Sum_{k=0..2*n+1} C(2*n+1,k)^2 * x^k]^2 ).

1, 3, 15, 125, 1033, 9385, 88531, 858739, 8517503, 85867417, 877145957, 9056393207, 94337137375, 990036525507, 10456495695277, 111048017798677, 1185005002916425, 12698840465721691, 136594962042690591, 1474203992211840997, 15958236903892529399, 173216891100594266403

Offset: 0

Author

Paul D. Hanna, Aug 30 2014

Keywords

• nonn

Comments

Self-convolution equals A246571.

Examples

			G.f.: A(x) = 1 + 3*x + 15*x^2 + 125*x^3 + 1033*x^4 + 9385*x^5 + 88531*x^6 +...
such that
A(x)^2 = 1/(1-x)^3 * (1 + x)^2 + x/(1-x)^7 * (1 + 3^2*x + 3^2*x^2 + x^3)^2
+ x^2/(1-x)^11 * (1 + 5^2*x + 10^2*x^2 + 10^2*x^3 + 5^2*x^4 + x^5)^2
+ x^3/(1-x)^15 * (1 + 7^2*x + 21^2*x^2 + 35^2*x^3 + 35^2*x^4 + 21^2*x^5 + 7^2*x^6 + x^7)^2 +...
Explicitly,
A(x)^2 = 1 + 6*x + 39*x^2 + 340*x^3 + 3041*x^4 + 28718*x^5 + 279987*x^6 +...+ A246571(n)*x^n +...
		

Crossrefs

Cf. A246563, A246570, A246571, A246572.

Programs

PARI

/* By definition: */
{a(n)=local(A=1); A = sqrt( sum(m=0, n, x^m/(1-x)^(4*m+3) * sum(k=0, 2*m+1, binomial(2*m+1, k)^2 * x^k)^2 +x*O(x^n)) ); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))