A211826 G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^5.

1, 1, 10, 190, 5080, 170080, 6724432, 303476320, 15300084160, 849174449680, 51341667458240, 3354970165353120, 235493617889171200, 17667618435092524160, 1410845692308772162560, 119491232651437498097920, 10700209630623386429434880, 1010278582501924072528588800

Offset: 0

Author

Paul D. Hanna, Apr 21 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 10*x^2 + 190*x^3 + 5080*x^4 + 170080*x^5 +...
Related expansions:
d/dx x*A(x) = 1 + 2*x + 30*x^2 + 760*x^3 + 25400*x^4 + 1020480*x^5 +...
A'(x) = 1 + 20*x + 570*x^2 + 20320*x^3 + 850400*x^4 + 40346592*x^5 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A112915, A211824, A211825.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*deriv(x*A)^5);polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))

Formula

G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^5.

a(n) ~ c * 5^n * n^(8/5) * n!, where c = 0.04375376183367762... - Vaclav Kotesovec, Aug 24 2017