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A062147
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Row sums of unsigned triangle A062137 (generalized a=3 Laguerre).
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7
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1, 5, 31, 229, 1961, 19081, 207775, 2501801, 32989969, 472630861, 7307593151, 121247816845, 2148321709561, 40476722545169, 807927483311551, 17028146983530961, 377844723929464865, 8803698102396787861, 214877019857456672479, 5482159931449737760181
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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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E.g.f.: exp(x/(1-x))/(1-x)^4.
a(n) = Sum_{m=0..n} n!*binomial(n+3, n-m)/m!.
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MAPLE
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A062147 := n -> n!*simplify(LaguerreL(n, 3, -1), 'LaguerreL');
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MATHEMATICA
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Table[Sum[n!*Binomial[n+3, n-k]/k!, {k, 0, n}], {n, 0, 20}]
(* or *)
Table[n!*SeriesCoefficient[E^(x/(1-x))/(1-x)^4, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 11 2012 *)
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PROG
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(PARI) my(x='x+O('x^66)); Vec(serlaplace(exp(x/(1-x))/(1-x)^4)) \\ Joerg Arndt, May 06 2013
(PARI) a(n) = vecsum(apply(abs, Vec(n!*pollaguerre(n, 3)))); \\ Michel Marcus, Feb 06 2021
(Magma) [Factorial(n)*(&+[Binomial(n+3, n-m)/Factorial(m): m in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018
(Sage) [factorial(n)*gen_laguerre(n, 3, -1) for n in (0..30)] # G. C. Greubel, Mar 10 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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