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A193425 E.g.f.: (1 - 2*x)^(-1/(1-x)). 1
1, 2, 12, 96, 976, 12000, 172608, 2838528, 52474112, 1076451840, 24254069760, 595235266560, 15801350443008, 451082627014656, 13778232107286528, 448348123661598720, 15483358506138009600, 565560454279135887360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

E.g.f.: exp( Sum_{n>=1} (2*x)^n/n * Sum_{k=0..n-1} 1/C(n-1,k) ).

E.g.f.: exp( Sum_{n>=1} 2*A126674(n)*x^n/n ), where A126674(n) = n!*Sum_{j=0..n-1} 2^j/(j+1).

a(n) ~ n!*n*2^n * (1 - 2*log(n)/n). - Vaclav Kotesovec, Jun 27 2013

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 12*x^2/2! + 96*x^3/3! + 976*x^4/4! + 12000*x^5/5! +...

where the logarithm involves sums of reciprocal binomial coefficients:

log(A(x)) = 2*x*(1) + (2*x)^2/2*(1 + 1) + (2*x)^3/3*(1 + 1/2 + 1) + (2*x)^4/4*(1 + 1/3 + 1/3 + 1) + (2*x)^5/5*(1 + 1/4 + 1/6 + 1/4 + 1) + (2*x)^6/6*(1 + 1/5 + 1/10 + 1/10 + 1/5 + 1) +...

Explicitly, the logarithm begins:

log(A(x)) = 2*x + 8*x^2/2! + 40*x^3/3! + 256*x^4/4! + 2048*x^5/5! + 19968*x^6/6! +...

in which the coefficients equal 2*A126674(n).

MATHEMATICA

CoefficientList[Series[(1-2*x)^(-1/(1-x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

PROG

(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, 2^m*x^m/m*sum(k=0, m-1, 1/binomial(m-1, k)))+x*O(x^n)), n)}

(PARI) {a(n)=n!*polcoeff((1-2*x+x*O(x^n))^(-1/(1-x)), n)}

CROSSREFS

Cf. A126674.

Sequence in context: A153231 A052564 A014297 * A206855 A219119 A052611

Adjacent sequences:  A193422 A193423 A193424 * A193426 A193427 A193428

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 27 2011

STATUS

approved

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)