A062191 Row sums of signed triangle A062138 (generalized a=5 Laguerre).

1, 5, 29, 191, 1405, 11389, 100585, 958271, 9758009, 105258005, 1191424981, 13996923775, 168226145269, 2023185762701, 23353840650785, 232509328597439, 1131674305674865, -36251185098769499, -1837042409174409971

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• sign
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062138.

Programs

Magma

m:=25; R:=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

Mathematica

Table[n!*LaguerreL[n, 5, 1], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)

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

PARI

my(x = 'x + O('x^30)); Vec(serlaplace(exp(-x/(1-x))/(1-x)^5)) \\  G. C. Greubel, May 11 2018

PARI

a(n) = vecsum(Vec(n!*pollaguerre(n, 5))); \\ Michel Marcus, Feb 06 2021

Formula

E.g.f.: exp(-x/(1-x))/(1-x)^5.

a(n) = Sum_{m=0..n} (-1)^m*n!*binomial(n+5, n-m)/m!.

Extensions

Typo in first formula corrected by Vaclav Kotesovec, Feb 25 2014