A199852 E.g.f. A(x) satisfies A(A(x)) = x * exp(2*x).

1, 2, 0, 4, -20, 36, 2296, -71280, 1347984, -9104480, -566853584, 26068456800, -109901066912, -42816208726368, 1570246237628160, 105861151925191936, -11551468847311923968, -237265887931262530560, 104987271408023239754752, -2079616585958181891671040

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..282

Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$, arXiv:1302.1986

Formula

a(n)=n!*T(n,1), T(n,m)=if n=m then 1 else 1/2((m^(n-m)*2^(n-m))/(n-m)!-sum(i=m+1..n-1, T(n,i)*T(i,m))).

Example

A(x) = x + x^2 + x^4/6 - x^5/6 + x^6/20 + 41*x^7/90 - 99*x^8/56 + ...

Crossrefs

Sequence in context: A320490 A326215 A248643 * A055978 A356189 A245695

Adjacent sequences: A199849 A199850 A199851 * A199853 A199854 A199855

Keyword

sign

Author

Vladimir Kruchinin, Nov 11 2011

Status

approved