A380493 a(n) = n! * Sum_{k=0..n} binomial(2*n+3,k)/(n-k)!.

1, 6, 57, 748, 12585, 259026, 6315001, 178134552, 5711078673, 205209960670, 8171229107481, 357235056697476, 17014791129640057, 877089297426429738, 48657292133825026905, 2890717184573264397616, 183125115830192864360481, 12323226433255671469949622

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

Formula

a(n) = n! * LaguerreL(n, n+3, -1).

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+4).

Prog

(PARI) a(n) = n!*pollaguerre(n, n+3, -1);

Crossrefs

Cf. A082545, A152059, A251568, A293985, A343832, A380491, A380492.

Sequence in context: A308863 A000406 A305276 * A032119 A294511 A242817

Adjacent sequences: A380490 A380491 A380492 * A380494 A380495 A380496

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2025

Status

approved