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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

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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

URL: https://oeis.org/A107593

⇱ A107593 - OEIS