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A190875
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E.g.f. exp(x+x^4)
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5
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1, 1, 1, 1, 25, 121, 361, 841, 21841, 184465, 912241, 3334321, 89824681, 1063799881, 7325422105, 36454050361, 1017339566881, 15314809967521, 134865698721121, 848781820990945, 24508030788375481, 443521231499750041, 4748434334677932361
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n)=n!*sum(j=0..n/3, binomial(n-3*j,j)/(n-3*j)!)
Recurrence: a(n) = a(n-1) + 4*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Jun 26 2013
a(n) ~ 2^(n/2-1)*exp(n^(1/4)/sqrt(2)-3*n/4)*n^(3*n/4). - Vaclav Kotesovec, Jun 26 2013
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MATHEMATICA
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CoefficientList[Series[E^(x+x^4), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)
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PROG
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(Maxima)
a(n):=n!*sum(binomial(n-3*j, j)/(n-3*j)!, j, 0, n/3);
(PARI) Vec(serlaplace(exp(x+x^4+O(x^66)))) /* Joerg Arndt, May 24 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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