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A062192
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Row sums of unsigned triangle A062138 (generalized a=5 Laguerre).
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6
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1, 7, 57, 529, 5509, 63591, 805597, 11109337, 165625929, 2654025319, 45481765921, 829903882017, 16062421776397, 328634683136839, 7086337847838789, 160604998959958441, 3816483607166825617
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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)^6.
a(n) = Sum_{m=0..n} n!*binomial(n+5, n-m)/m!.
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MAPLE
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A062192:= n -> n!*simplify(LaguerreL(n, 5, -1), 'LaguerreL');
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MATHEMATICA
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Table[Sum[n! Binomial[n+5, n-m]/m!, {m, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Apr 11 2012 *)
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PROG
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(PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+5, n); g=1; a+=sum(m=1, n, f*binomial(n+5, n-m)/g*=m); write("b062192.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x/(1-x))/(1-x)^6)) \\ G. C. Greubel, Feb 06 2018
(PARI) a(n) = vecsum(apply(abs, Vec(n!*pollaguerre(n, 5)))); \\ Michel Marcus, Feb 06 2021
(Magma) [Factorial(n)*(&+[Binomial(n+5, n-m)/Factorial(m): m in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018
(Sage) [factorial(n)*gen_laguerre(n, 5, -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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