A089449 Antidiagonal sums of square table A089447, which lists the coefficients of x^n*y^k in f(x,y) that satisfies: f(x,y) = g(x,y) + xy*f(x,y)^4 and where g(x,y) satisfies: 1 + (x+y-1)*g(x,y) + xy*g(x,y)^2 = 0.

1, 2, 6, 22, 90, 396, 1837, 8870, 44186, 225628, 1175322, 6222788, 33392644, 181216728, 992829379, 5483790870, 30502513970, 170705626308, 960498281302, 5430200987260, 30830681187480, 175715526842056, 1004931956037782

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x) = sum(n>=0, Catalan(n+1)*x^n) + x^2*A(x)^4, where Catalan(n)=(2n)!/(n!*(n+1)!).

From Vaclav Kotesovec, Oct 10 2020: (Start)

G.f.: A(x) = (1 - Sqrt[1-4*x] - 2*x)/(2*x^2) + x^2*A(x)^4.

a(n) ~ sqrt(11) * 3^(15/2 + 3*n) / ((8 + 3*sqrt(3) + 4*sqrt(4 + 3*sqrt(3))) * sqrt((2519 + 528*sqrt(3) + 2*sqrt(1484692 + 881529*sqrt(3))) * Pi) * n^(3/2) * 2^(2*n + 5/2) * (-32 - 18*sqrt(3) + sqrt(1996 + 1233*sqrt(3)))^(n+2)). (End)

Crossrefs

Cf. A089447 (table), A089448 (diagonal), A002293.

Sequence in context: A165546 A279568 A053617 * A264601 A308564 A226435

Adjacent sequences: A089446 A089447 A089448 * A089450 A089451 A089452

Keyword

nonn

Author

Paul D. Hanna, Nov 02 2003

Status

approved