A302688 Expansion of 1 + x*(1 + 2*x*(1 + 3*x*(1 + 4*x*(1 + 5*x*(1 + ...)^5)^4)^3)^2).

1, 1, 2, 12, 162, 3888, 144768, 7693920, 551981520, 51355426992, 6010929609408, 864202875949440, 149698423474606080, 30747550680449611200, 7388611598645058636000, 2053517715502048081023360, 653614372412684344833419520, 236202930442590804658824312960

Offset: 0

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

• nonn

Comments

(a(n) / n!^2)^(1/n) tends to 1.36594... - Vaclav Kotesovec, Apr 12 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A095793, A128318, A128319, A138211, A138212.

Programs

Mathematica

nmax = 17; CoefficientList[Series[1 + x Fold[((#2 + 1) x #1 + 1)^#2 &, 0, Reverse[Range[nmax]]], {x, 0, nmax}], x]

Formula

G.f. A(x) = 1 + x + 2*x^2 + 12*x^3 + 162*x^4 + 3888*x^5 + 144768*x^6 + 7693920*x^7 + 551981520*x^8 + ...