A361539 a(n) = A361540(n, n-2) for n >= 2, a diagonal of triangle A361540.

3, 39, 426, 4550, 50085, 577731, 7022596, 90148860, 1222753815, 17515226465, 264663151038, 4212100028994, 70475063838361, 1237144088015535, 22735980569119560, 436467520716475064, 8733235757816095083, 181740089309026259565, 3925458146197916823970

Offset: 2

Author

Paul D. Hanna, Mar 20 2023

Keywords

• nonn

Comments

E.g.f. F(x,y) of triangle A361540 satisfies the following.

(1) F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n!.

(2) F(x,y) = Sum_{n>=0} F(x,y)^(n^2) * exp(y*x*F(x,y)^n) * x^n/n!.

The diagonal above this one in triangle A361540 has e.g.f. x*exp(x)*exp(x*exp(x)).

Examples

			E.g.f. A(x) = 3*x^2/2! + 39*x^3/3! + 426*x^4/4! + 4550*x^5/5! + 50085*x^6/6! + 577731*x^7/7! + 7022596*x^8/8! + 90148860*x^9/9! + 1222753815*x^10/10! + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 2..42

Crossrefs

Cf. A361540.

Programs

PARI

/* E.g.f. of triangle A361540 is F(x,y) = Sum_{n>=0} (F(x,y)^n + y)^n * x^n/n! */
{A361540(n,k) = my(A = 1); for(i=1,n, A = sum(m=0, n, (A^m + y +x*O(x^n))^m * x^m/m! )); n!*polcoeff(polcoeff(A, n,x),k,y)}
for(n=2, 20, print1(A361540(n,n-2), ", "))