A259612 G.f. A(x) satisfies: A(x)*A'(x) = Series_Reversion( x - 2*x*A(x)*A'(x) - A(x)^2 ).

1, 1, 6, 58, 720, 10506, 172284, 3092717, 59758608, 1228626514, 26657057728, 606616602302, 14410894287172, 356081682054300, 9124705519233832, 241916247567814448, 6622686675121529288, 186900262172114801748, 5429779249015331564288, 162190080378495122207760

Offset

1,3

Comments

Self-convolution yields A259611.

Links

Table of n, a(n) for n=1..20.

Example

 G.f. A(x) = x + x^2 + 6*x^3 + 58*x^4 + 720*x^5 + 10506*x^6 + 172284*x^7 +...
where
A(x)*A'(x) = x + 3*x^2 + 26*x^3 + 320*x^4 + 4776*x^5 + 81018*x^6 + 1510336*x^7 + 30328173*x^8 +...+ A259610(n)*x^n +...
also
A(x)^2 = x^2 + 2*x^3 + 13*x^4 + 128*x^5 + 1592*x^6 + 23148*x^7 + 377584*x^8 + 6739594*x^9 +...+ A259611(n)*x^n +...

Prog

 (PARI) {a(n)=local(A=x^2); for(i=0, n, A = 2*intformal( serreverse(x - x*A' - A +x*O(x^n)))); polcoeff(sqrt(A), n)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A259610, A259611.

Sequence in context: A073848 A141382 A212426 * A305599 A316653 A302598

Adjacent sequences: A259609 A259610 A259611 * A259613 A259614 A259615

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2015

Status

approved