A062265 - OEIS

%I #22 Jan 15 2024 17:17:36

%S 1,4,19,104,641,4364,32251,254176,2091841,17435924,138844931,

%T 891248984,263059969,-163754125796,-4970760027029,-117798281164336,

%U -2588474951884159,-55489648295242204,-1184521077396558989,-25406942370946446776,-549455868757454486399,-11980725887273702949076

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

%H G. C. Greubel, <a href="/A062265/b062265.txt">Table of n, a(n) for n = 0..445</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) = n! * Sum_{m=0..n} (-1)^m * binomial(n+4, n-m)/m!.

%F a(n) = 2*(n+1)*a(n-1) - (n-1)*(n+3)*a(n-2). - _Vaclav Kotesovec_, Aug 01 2013

%t Table[n!*LaguerreL[n, 4, 1],{n,0,20}] (* _Vaclav Kotesovec_, Aug 01 2013 *)

%o (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

%o (PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 4))); \\ _Michel Marcus_, Feb 06 2021

%o (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

%Y Cf. A062140.

%K sign,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001