A371114 a(n) is n! times the coefficient of x in the associated Laguerre polynomial Laguerre(n,x,1).

0, 1, 1, -1, -16, -111, -691, -4145, -23080, -96159, 195137, 13914911, 284958904, 4842967921, 77613841629, 1219132694767, 19006810258064, 294117291312577, 4469910552829473, 64942899785556031, 841752172982238304, 7465153745073705041, -61832090598783228403, -6408471053640082778097

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = n!*Sum_{k=0..n-1} A009940(k)/(k!*(n-k)).

a(n) = (4*n - 7)*a(n-1) - (6*n^2 - 25*n + 27)*a(n-2) + (n-2)*(4*n^2 - 21*n + 28)*a(n-3) - (n-3)^3*(n-2)*a(n-4). - Vaclav Kotesovec, Mar 12 2024

Mathematica

a[n_]:=n! D[LaguerreL[n, x, 1], x]/.{x->0}; Array[a, 25, 0]
Table[n! Sum[LaguerreL[k, 1]/(n-k), {k, 0, n-1}], {n, 0, 25}]
RecurrenceTable[{(-3 + n)^3*(-2 + n)*a[n-4] - (-2 + n)*(28 - 21*n + 4*n^2)*a[n-3] + (27 - 25*n + 6*n^2)*a[n-2] + (7 - 4*n)*a[n-1] + a[n] == 0, a[0] == 0, a[1] == 1, a[2] == 1, a[3] == -1}, a, {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2024 *)

Prog

(PARI) a(n) = n!*sum(k=0, n-1, pollaguerre(k, 0, 1)/(n-k)); \\ Michel Marcus, Mar 12 2024

Crossrefs

Cf. A009940.

Sequence in context: A234250 A240786 A213754 * A279425 A144449 A035016

Adjacent sequences: A371111 A371112 A371113 * A371115 A371116 A371117

Keyword

sign

Author

Rui Xian Siew, Mar 10 2024

Status

approved