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A112243 Expansion of exp(x(1+x)/(1-2x)). 0
1, 1, 7, 55, 577, 7441, 113671, 2003527, 39971905, 889608097, 21834577351, 585555975511, 17027451783937, 533460597334705, 17908302027585607, 641152804988733031, 24380543011087797121, 981149507717921468737 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

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

FORMULA

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

a(n) ~ 3^(1/4) * 2^(n-1) * n^(n-1/4) * exp(sqrt(3*n)-n-5/8). - Vaclav Kotesovec, Sep 25 2013

Conjecture: a(n) +(-4*n+3)*a(n-1) +2*(n-1)*(2*n-5)*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Feb 20 2015

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[(x(x+1))/(1-2x)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 21 2011 *)

CROSSREFS

Sequence in context: A094905 A178922 A306046 * A083836 A326885 A159313

Adjacent sequences:  A112240 A112241 A112242 * A112244 A112245 A112246

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 29 2005

STATUS

approved

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Last modified January 15 12:14 EST 2021. Contains 340187 sequences. (Running on oeis4.)