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A202832
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E.g.f: exp(2*x + 5*x^2/2).
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2
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1, 2, 9, 38, 211, 1182, 7639, 50738, 368841, 2767202, 22132249, 182624598, 1582522891, 14122521662, 131109031239, 1250794578818, 12334766500561, 124733099306562, 1297921351160809, 13821821639912198, 150946171640101251, 1684074507271422302, 19217497036753475959
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..[n/2]} 2^(n-3*k)*5^k * n!/((n-2*k)!*k!).
O.g.f.: 1/(1-2*x - 5*x^2/(1-2*x - 10*x^2/(1-2*x - 15*x^2/(1-2*x - 20*x^2/(1-2*x -...))))), a continued fraction.
a(n) ~ exp(2/5*sqrt(5*n)-n/2-1/5)*5^(n/2)*n^(n/2)/sqrt(2)*(1+17/150*sqrt(5)/sqrt(n)). - Vaclav Kotesovec, Oct 20 2012
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EXAMPLE
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E.g.f.: 1 + 2*x + 9*x^2/2! + 38*x^3/3! + 211*x^4/4! + 1182*x^5/5! +...
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MATHEMATICA
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CoefficientList[Series[E^(2*x+5*x^2/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 20 2012 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(exp(2*x+5*x^2/2+x*O(x^n)), n)}
(PARI) {a(n)=sum(k=0, n\2, 2^(n-3*k)*5^k*n!/((n-2*k)!*k!))}
(PARI) /* O.g.f. as a continued fraction: */
{a(n)=local(CF=1+2*x+x*O(x^n)); for(k=1, n-1, CF=1/(1-2*x-5*(n-k)*x^2*CF)); polcoeff(CF, n)}
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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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