OFFSET
0,3
COMMENTS
Self-convolution equals A246570.
FORMULA
G.f.: A(x) = 1 + x + 7*x^2 + 51*x^3 + 425*x^4 + 3879*x^5 + 36527*x^6 +...
such that
A(x)^2 = 1/(1-x) + x/(1-x)^5 * (1 + 2^2*x + x^2)^2
+ x^2/(1-x)^9 * (1 + 4^2*x + 6^2*x^2 + 4^2*x^3 + x^4)^2
+ x^3/(1-x)^13 * (1 + 6^2*x + 15^2*x^2 + 20^2*x^3 + 15^2*x^4 + 6^2*x^5 + x^6)^2 +...
Explicitly,
A(x)^2 = 1 + 2*x + 15*x^2 + 116*x^3 + 1001*x^4 + 9322*x^5 + 89363*x^6 +...+ A246570(n)*x^n +...
PROG
(PARI) /* By definition: */
{a(n)=local(A=1); A = sqrt( sum(m=0, n, x^m/(1-x)^(4*m+1) * sum(k=0, 2*m, binomial(2*m, k)^2 * x^k)^2 +x*O(x^n)) ); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 30 2014
STATUS
approved