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A112240 Expansion of exp(x/(1-x-2x^2)). 0
1, 1, 3, 25, 217, 2541, 34531, 550453, 9957585, 202137337, 4543312771, 112004037201, 3003936136873, 87057179039845, 2710682505789987, 90230919126896941, 3197152300287286561, 120131212083966304113 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In general, e.g.f. exp(x/(1-ax-bx^2)) has general term n!*sum{i=0..n, sum{j=0..n, a^j*(b/a)^(n-i-j)*C(i+j-1,j) C(j,n-i-j)/i!}}.

LINKS

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

FORMULA

E.g.f. exp(x/(1-x-x^2)); a(n)=n!*sum{i=0..n, sum{j=0..n, 2^(n-i-j)* C(i+j-1,j) C(j, n-i-j)/i!}};

a(n) = (2*n-1)*a(n-1) + 3*(n-2)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*(2*n-7)*a(n-3) - 4*(n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Sep 25 2013

a(n) ~ 3^(-1/4) * n^(n-1/4) * 2^(n-1/2) * exp(2*sqrt(n/3)-n-1/18) * (1 - 263/(432*sqrt(3*n))). - Vaclav Kotesovec, Sep 25 2013

MATHEMATICA

CoefficientList[Series[E^(x/(1-x-2*x^2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)

CROSSREFS

Sequence in context: A280970 A222052 A230718 * A155640 A024217 A199679

Adjacent sequences:  A112237 A112238 A112239 * A112241 A112242 A112243

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 29 2005

STATUS

approved

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Last modified January 22 14:06 EST 2021. Contains 340362 sequences. (Running on oeis4.)