A107592 G.f. satisfies: A(x)^2 = Sum_{n>=0} x^n * A(x)^((n+1)*(n+2)/2).

1, 1, 3, 13, 67, 382, 2327, 14855, 98208, 667180, 4632647, 32751382, 235072482, 1709232902, 12568852562, 93348649555, 699485096637, 5283685539096, 40205412111227, 308020225286402, 2374795521493354, 18419175004781334

Offset

0,3

Links

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

Formula

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

G.f. A(x) = (1/x)*series-reversion(x/G(x)) and thus A(x) = G(x*A(x)) where G(x) is the g.f. of A107591.

Example

A^2 = A + x*A^3 + x^2*A^6 + x^3*A^10 + x^4*A^15 + x^5*A^21 ...
= (1 + x + 3*x^2 + 13*x^3 + 67*x^4 + 382*x^5 + 2327*x^6 +...)
+ (x + 3*x^2 + 12*x^3 + 58*x^4 + 315*x^5 + 1848*x^6 +...)
+ (x^2 + 6*x^3 + 33*x^4 + 188*x^5 + 1122*x^6 +...)
+ (x^3 + 10*x^4 + 75*x^5 + 520*x^6 +...)
+ (x^4 + 15*x^5 + 150*x^6 +...) +...
= 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, n)}

Crossrefs

Cf. A107590, A107591, A107593 (self-convolution).

Sequence in context: A062992 A064062 A114191 * A215257 A367919 A350855

Adjacent sequences: A107589 A107590 A107591 * A107593 A107594 A107595

Keyword

eigen,nonn

Author

Paul D. Hanna, May 17 2005

Status

approved