A302657 a(n) = [x^n] 1 + x*(1 + 2*x*(1 + 3*x*(1 + 4*x*(1 + 5*x*(1 + ...)^n)^n)^n)^n)^n.

1, 1, 4, 66, 2576, 181580, 20040132, 3176873014, 683004260416, 191131280146584, 67496202291859460, 29358012892996082966, 15422766301341408798384, 9628365732822661693594804, 7046590639669984518105404260, 5975695685335003337179698967230, 5813189543201787075970895280603392

Offset: 0

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

• nonn

Comments

(a(n) / (n-1)!^2)^(1/n) tends to 4.3002... - Vaclav Kotesovec, Apr 11 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000142, A128318, A128319, A302686.

Programs

Mathematica

Table[SeriesCoefficient[1 + x Fold[((#2 + 1) x #1 + 1)^n &, 0, Reverse[Range[n]]], {x, 0, n}], {n, 0, 16}]