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

Author

Seiichi Manyama, Jan 25 2025

Keywords

• nonn

Links

• Wikipedia, Laguerre polynomials
• Index entries for sequences related to Laguerre polynomials

Crossrefs

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

Programs

PARI

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

Formula

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

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