A062265 Row sums of signed triangle A062140 (generalized a=4 Laguerre).

1, 4, 19, 104, 641, 4364, 32251, 254176, 2091841, 17435924, 138844931, 891248984, 263059969, -163754125796, -4970760027029, -117798281164336, -2588474951884159, -55489648295242204, -1184521077396558989, -25406942370946446776, -549455868757454486399, -11980725887273702949076

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062140.

Programs

Magma

[Factorial(n)*(&+[(-1)^k*Binomial(n+4,n-k)/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 13 2018

Mathematica

Table[n!*LaguerreL[n, 4, 1],{n,0,20}] (* Vaclav Kotesovec, Aug 01 2013 *)

PARI

for(n=0,30, print1(n!*sum(k=0,n, (-1)^k*binomial(n+4,n-k)/k!), ", ")) \\ G. C. Greubel, May 13 2018

PARI

a(n) = vecsum(Vec(n!*pollaguerre(n, 4))); \\ Michel Marcus, Feb 06 2021

Formula

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

a(n) = n! * Sum_{m=0..n} (-1)^m * binomial(n+4, n-m)/m!.

a(n) = 2*(n+1)*a(n-1) - (n-1)*(n+3)*a(n-2). - Vaclav Kotesovec, Aug 01 2013