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A112242
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E.g.f. exp( x*(1+x)/(1-x) ).
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2
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1, 1, 5, 25, 169, 1361, 12781, 136585, 1633745, 21594529, 312239701, 4898379641, 82810239865, 1500015354865, 28970936174909, 594083320767721, 12886811207794081, 294742414455540545, 7087332775240107685, 178707496551303048409, 4714241296084031285321, 129830157857411005318801
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OFFSET
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0,3
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COMMENTS
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In general, e.g.f. exp(x*(1+a*x)/(1-b*x)) 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!}}.
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LINKS
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FORMULA
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E.g.f.: exp(x(1+x)/(1-x).
a(n) = sum{i=0..n, sum{j=0..n, C(i, j)*C(n-j-1, n-i-j)*n!/i!}};
D-finite with recurrence: a(n) = (2*n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Jun 27 2013
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MATHEMATICA
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Range[0, 18]!*CoefficientList[ Series[ Exp[x(1+x)/(1-x)], {x, 0, 18}], x] - Zerinvary Lajos, Mar 23 2007
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PROG
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(PARI)
x='x+O('x^33);
Vec(serlaplace(exp( x*(1+x)/(1-x) )))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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