A372492 G.f. satisfies A(A(A(A(x)))) = F(x), where F(x) is the g.f. for A002697(n) = n*4^(n-1).

0, 1, 2, 0, 4, -8, -8, 288, -1712, -1888, 105472, -288576, -10404800, 84940672, 1454871936, -24372060160, -255228956416, 8232158755328, 49829958005760, -3390379506089984, -7038865141000192, 1699612131395493888, -3459036721655810048, -1025681798088053424128

Offset: 0

Author

Seiichi Manyama, May 03 2024

Keywords

• sign

Examples

			B(x) = x + 4*x^2 + 8*x^3 + 16*x^4 + 32*x^5 + 256*x^7 + 768*x^8 - 14848*x^9 + 51200*x^10 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..435
• Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986 [math.CO], 2013.

Crossrefs

Cf. A002697, A309509.

Formula

Let B(x) = A(A(x)). B(B(x)) = F(x).

B(x) = G(2*x)/2, where G(x) is the g.f. for A309509.