A107593 Self-convolution of A107592.

1, 2, 7, 32, 169, 976, 5989, 38398, 254509, 1731596, 12032874, 85092944, 610714311, 4439136084, 32626373027, 242153129074, 1813069499846, 13682961621602, 104014376985334, 796004610604094, 6129901459731357, 47484532009772272

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^((n+1)*(n+2)/4).

G.f. A(x) = (1/x)*series-reversion(x/G(x)^2) and thus A(x) = G(x*A(x))^2 where G(x) is the g.f. of A107590.

Example

A = A^(1/2) + x*A^(3/2) + x^2*A^(6/2) + x^3*A^(10/2) +...
= 1 + 2*x + 7*x^2 + 32*x^3 + 169*x^4 + 976*x^5 + 5989*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^((j+1)*(j+2)/2-1)+x*O(x^n))); polcoeff(A^2, n)}

Crossrefs

Cf. A107590, A107591, A107592.

Sequence in context: A006781 A330075 A115197 * A125277 A321688 A222013

Adjacent sequences: A107590 A107591 A107592 * A107594 A107595 A107596

Keyword

nonn

Author

Paul D. Hanna, May 17 2005

Status

approved