A361549 a(n) = A361540(n,2) for n >= 2, a column of triangle A361540.

1, 18, 426, 12040, 401355, 15456756, 676130644, 33151425840, 1802216703285, 107652497473180, 7012494336544686, 494963689847333928, 37648456802884402111, 3071415347513049808740, 267644521958509484952360, 24822151072519637091258976, 2442314922307988498911793385

Offset

2,2

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!.

Column 0 near to this one in triangle A361540 has e.g.f. G(x) = Sum_{n>=0} G(x)^(n^2)*x^n/n!.

Links

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

Example

E.g.f.: A(x) = x^2/2! + 18*x^3/3! + 426*x^4/4! + 12040*x^5/5! + 401355*x^6/6! + 15456756*x^7/7! + 676130644*x^8/8! + 33151425840*x^9/9! + 1802216703285*x^10/10! + ... + a(n)*x^n/n! + ...
a(n) is divisible by n*(n-1)/2, where a(n)*2/(n*(n-1)) begins
[1, 6, 71, 1204, 26757, 736036, 24147523, 920872940, 40049260073, ...].

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(F = 1); for(i=1, n, F = sum(m=0, n, (F^m + y +x*O(x^n))^m * x^m/m! )); n!*polcoeff(polcoeff(F, n, x), k, y)}
for(n=2, 20, print1(A361540(n, 2), ", "))

Crossrefs

Cf. A361540, A361544.

Sequence in context: A215229 A172135 A005477 * A326368 A197343 A289941

Adjacent sequences: A361546 A361547 A361548 * A361550 A361551 A361552

Keyword

nonn

Author

Paul D. Hanna, Mar 20 2023

Status

approved