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

0,2

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

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

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 *)

Prog

(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
(Magma) [(&+[Factorial(n)*Binomial(n+4, n-m)/Factorial(m): m in [0..n]]): n in [0..20]]; // G. C. Greubel, Feb 06 2018
(Sage) [factorial(n)*gen_laguerre(n, 4, -1) for n in (0..30)] # G. C. Greubel, Mar 10 2021

Crossrefs

Cf. A062140, A216294.

Sequence in context: A220097 A090010 A176732 * A217485 A337555 A290783

Adjacent sequences: A062263 A062264 A062265 * A062267 A062268 A062269

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved