OFFSET
0,2
FORMULA
log(a(n)) ~ log(BarnesG(n+2)) + 4*n^(3/2)/3 - n*log(n)/4 - (1/4 + log(2) + log(Pi)/2)*n + 55*sqrt(n)/24.
log(a(n)) ~ n^2*log(n)/2 - 3*n^2/4 + 4*n^(3/2)/3 + 3*n*log(n)/4 - (5/4 + log(2)/2)*n + 55*sqrt(n)/24.
MATHEMATICA
Table[Product[k! * LaguerreL[k, -1], {k, 1, n}], {n, 0, 15}]
Table[BarnesG[n+2] * Product[LaguerreL[k, -1], {k, 1, n}], {n, 0, 15}]
PROG
(Python)
from math import prod, factorial, comb
def A365269(n): return prod(sum(factorial(m)*comb(k, m)**2 for m in range(k+1)) for k in range(1, n+1)) # Chai Wah Wu, Aug 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 30 2023
STATUS
approved