A272461 G.f. A(x) satisfies: A( x - A(x^4)/x^2 ) = x.

1, 1, 2, 5, 14, 43, 140, 474, 1650, 5865, 21194, 77623, 287492, 1074915, 4051824, 15381073, 58749102, 225621404, 870686810, 3374625925, 13130575110, 51271434788, 200845390668, 789081913225, 3108496250028, 12275905239752, 48590260462470, 192736593501813, 766007363990640, 3049978926971396, 12164745517874576, 48596364360237882, 194426663474794450, 778968350863994065

Offset: 1

Author

Paul D. Hanna, Apr 29 2016

Keywords

• nonn

Examples

			G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 + 474*x^8 + 1650*x^9 + 5865*x^10 + 21194*x^11 + 77623*x^12 +...
where A( x - A(x^4)/x^2 ) = x.
RELATED SERIES.
Let B(x) be the series reversion of the g.f. A(x) so that A(B(x)) = x, then
B(x) = x - x^2 - x^6 - 2*x^10 - 5*x^14 - 14*x^18 - 43*x^22 - 140*x^26 - 474*x^30 - 1650*x^34 - 5865*x^38 - 21194*x^42 - 77623*x^46 +...
such that B(x) = x - A(x^4)/x^2.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A141200, A272460.

Programs

PARI

{a(n) = my(A=x); for(i=1,n, A = serreverse( x - subst(A,x,x^4 +x^3*O(x^n))/x^2 )); polcoeff(A,n)}
for(n=1,50,print1(a(n),", "))

Formula

a(n) ~ c * d^n / n^(3/2), where d = 4.1920029654932692520828... and c = 0.1046247209912855075794... . - Vaclav Kotesovec, May 03 2016