A062266 Row sums of unsigned triangle A062140 (generalized a=4 Laguerre).

1, 6, 43, 358, 3393, 36046, 424051, 5470158, 76751233, 1163391958, 18941512731, 329604456886, 6103575192193, 119823200043678, 2485452283923043, 54309931242376606, 1246803623807490561, 29999359707124127398, 754865494585690965643, 19824604328577866107398

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Luis Verde-Star, A Matrix Approach to Generalized Delannoy and Schröder Arrays, J. Int. Seq., Vol. 24 (2021), Article 21.4.1.
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062140, A216294.

Programs

Magma

[(&+[Factorial(n)*Binomial(n+4,n-m)/Factorial(m): m in [0..n]]): n in [0..20]]; // G. C. Greubel, Feb 06 2018

Maple

A062266:= n -> n!*simplify(LaguerreL(n,4,-1), 'LaguerreL');
seq(A062266(n), n = 0 .. 30); # G. C. Greubel, Mar 10 2021

Mathematica

Table[n!*SeriesCoefficient[E^(x/(1-x))/(1-x)^5,{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 11 2012 *)
With[{nn=20},CoefficientList[Series[Exp[x/(1-x)]/(1-x)^5,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 11 2025 *)

PARI

my(x='x+O('x^66)); Vec(serlaplace(exp(x/(1-x))/(1-x)^5)) \\ Joerg Arndt, May 06 2013

PARI

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

Sage

[factorial(n)*gen_laguerre(n, 4, -1) for n in (0..30)] # G. C. Greubel, Mar 10 2021

Formula

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

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

a(n) = 2*(n+2)*a(n-1) - (n-1)*(n+3)*a(n-2). - Vaclav Kotesovec, Oct 11 2012

a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n+9/4)/sqrt(2). - Vaclav Kotesovec, Oct 11 2012

a(n) = n!*LaguerreL(n, 4, -1). - G. C. Greubel, Mar 10 2021