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%I #23 Sep 08 2022 08:45:03
%S 1,5,29,191,1405,11389,100585,958271,9758009,105258005,1191424981,
%T 13996923775,168226145269,2023185762701,23353840650785,
%U 232509328597439,1131674305674865,-36251185098769499,-1837042409174409971
%N Row sums of signed triangle A062138 (generalized a=5 Laguerre).
%H Harry J. Smith, <a href="/A062191/b062191.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F E.g.f.: exp(-x/(1-x))/(1-x)^5.
%F a(n) = Sum_{m=0..n} (-1)^m*n!*binomial(n+5, n-m)/m!.
%t Table[n!*LaguerreL[n, 5, 1], {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 25 2014 *)
%o (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, ((-1)^m)*f*binomial(n+5, n-m)/g*=m); write("b062191.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 02 2009
%o (PARI) my(x = 'x + O('x^30)); Vec(serlaplace(exp(-x/(1-x))/(1-x)^5)) \\ _G. C. Greubel_, May 11 2018
%o (PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 5))); \\ _Michel Marcus_, Feb 06 2021
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^5)); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 11 2018
%Y Cf. A062138.
%K sign,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 19 2001
%E Typo in first formula corrected by _Vaclav Kotesovec_, Feb 25 2014
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