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

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..100

Index entries for sequences related to Laguerre polynomials

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

Mathematica

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

Prog

(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
(Magma) m:=25; R<x>:=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

Crossrefs

Cf. A062137.

Sequence in context: A295539 A359120 A174347 * A216947 A090365 A035009

Adjacent sequences: A062143 A062144 A062145 * A062147 A062148 A062149

Keyword

sign,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved