A302102 G.f. A(x) satisfies: A(x) = 1 + x * (x*A(x)^4)' / (x*A(x))'.

1, 1, 6, 60, 796, 12873, 243648, 5274630, 128693820, 3501032280, 105278025690, 3473075317080, 124851287129604, 4860913404292030, 203839755469977840, 9161170785398640570, 439317870410796482460, 22390147212903891054540, 1208526686930226056003640, 68866979112831866042953128, 4131396903316522288744806384, 260262349821990852529147365849

Offset: 0

Author

Paul D. Hanna, Apr 07 2018

Keywords

• nonn

Comments

Compare to: C(x) = 1 + x * (x*C(x)^2)' / (x*C(x))' holds when C(x) = 1 + x*C(x)^2, which is a g.f. of the Catalan numbers (A000108).

Compare to: G(x) = 1 + x * (x*G(x)^3)' / (x*G(x))' holds when G(x) = 1/(1 - x*G(x)/(1 - 2*x*G(x)/(1 - 3*x*G(x)/(1 - ...)))), a continued fraction, which is the g.f. of A301363.

Examples

			G.f.: A(x) = 1 + x + 6*x^2 + 60*x^3 + 796*x^4 + 12873*x^5 + 243648*x^6 + 5274630*x^7 + 128693820*x^8 + 3501032280*x^9 + 105278025690*x^10 + ...
such that A(x) = 1 + x * (x*A(x)^4)' / (x*A(x))'.
		

Crossrefs

Cf. A301363, A302101.

Programs

PARI

/* Differential Equation */
{a(n) = my(A=1); for(i=0,n, A = 1 + x*(x*A^4)'/(x*A +x^2*O(x^n))'); polcoeff(A,n)}
for(n=0, 30, print1(a(n),", "))

Formula

G.f. A(x) satisfies: A(x) = 1 + x*A(x)^3 * (A(x) + 4*x*A'(x)) / (A(x) + x*A'(x)).