OFFSET
0,3
COMMENTS
Related to the coefficient triangle of generalized Laguerre polynomials A021009.
FORMULA
Sum_{n>=0} a(n) * x^n / n!^3 = BesselJ(0,2*sqrt(x)) * Sum_{n>=0} x^n / n!^3. - Ilya Gutkovskiy, Jun 19 2022
MAPLE
T := proc(n, k) local S; S := proc(n, k) option remember;
`if`(k = 0, 1, `if`(k > n, 0, S(n-1, k-1)/k + S(n-1, k))) end: n!*S(n, k) end:
a := n -> add((-1)^(n-j)*T(n, j)*binomial(n, j), j=0..n): seq(a(n), n=0..20);
PROG
(PARI) rowT(n) = Vecrev(n!*pollaguerre(n)); \\ A021009
a(n) = my(v=rowT(n)); sum(k=0, n, (-1)^(n-k)*binomial(n, k)*abs(v[k+1])); \\ Michel Marcus, May 04 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, May 04 2021
STATUS
approved