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

2,1

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)).

Links

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

Example

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! + ...

Prog

(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), ", "))

Crossrefs

Cf. A361540.

Sequence in context: A203243 A063035 A198970 * A014850 A341671 A328809

Adjacent sequences: A361536 A361537 A361538 * A361540 A361541 A361542

Keyword

nonn

Author

Paul D. Hanna, Mar 20 2023

Status

approved