A062146 Row sums of signed triangle A062137 (generalized Laguerre, a=3).

1, 3, 11, 47, 225, 1159, 6067, 28419, 58433, -1390645, -35514309, -636045257, -10431927839, -167173905393, -2678202265885, -43236880758901, -703702453254783, -11485574113211501, -185707408082199317, -2901041900411825985

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. A062137.

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^4)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018

Mathematica

Table[n!*LaguerreL[n, 3, 1],{n,0,20}] (* Vaclav Kotesovec, Aug 01 2013 *)

PARI

{ f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+3, n); g=1; a+=sum(m=1, n, ((-1)^m)*f*binomial(n+3, n-m)/g*=m); write("b062146.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009

PARI

my(x='x+O('x^30)); Vec(exp(-x/(1-x))/(1-x)^4) \\ G. C. Greubel, May 11 2018

PARI

a(n) = vecsum(Vec(n!*pollaguerre(n, 3))); \\ Michel Marcus, Feb 06 2021

Formula

E.g.f.: exp(-x/(1-x))/(1-x)^4.

a(n) = sum(((-1)^m)*n!*binomial(n+3, n-m)/m!, m=0..n).

a(n) = (2*n+1)*a(n-1) - (n-1)*(n+2)*a(n-2). - Vaclav Kotesovec, Aug 01 2013