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A220112 E.g.f. A(x) satisfies A(A(x))=(1/4)*log(1/(1-4*x)). 0
1, 2, 10, 80, 872, 11928, 195072, 3702080, 80065792, 1950808000, 53016791360, 1587229842688, 51619520360960, 1808576831681536, 68562454975587328, 2830905156661645312, 124395772159835529216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..17.

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

FORMULA

a(n)=T(n,1), T(n,m)=1/2*(4^(n-m)*(-1)^(n-m)*stirling1(n,m)-sum(i=m+1..n-1, T(n,i)*T(i,m))), T(n,n)=1.

MATHEMATICA

t[n_, m_] := t[n, m] = 1/2*(4^(n - m)*(-1)^(n - m)*StirlingS1[n, m] - Sum[t[n, i]*t[i, m], {i, m+1, n-1}]); t[n_, n_] = 1; Table[t[n, 1], {n, 1, 17}] (* Jean-Fran├žois Alcover, Feb 22 2013 *)

PROG

(Maxima)

T(n, m):=if n=m then 1 else 1/2*(4^(n-m)*(-1)^(n-m)*stirling1(n, m)-sum(T(n, i)*T(i, m), i, m+1, n-1));

makelist((T(n, 1)), n, 1, 10);

CROSSREFS

Sequence in context: A003578 A274276 A152600 * A048286 A227463 A008544

Adjacent sequences:  A220109 A220110 A220111 * A220113 A220114 A220115

KEYWORD

nonn

AUTHOR

Dmitry Kruchinin, Dec 05 2012

STATUS

approved

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Last modified July 31 15:10 EDT 2021. Contains 346374 sequences. (Running on oeis4.)