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A349067 a(n) = H(3*n, n), where H(n,x) is n-th Hermite polynomial. 3
1, -4, -824, -406944, 854857408, 36727035808000, 1350597603460566528, 70169228831160001808384, 5261285254051930823802720256, 556216363355718012207356567863296, 80574670961706857240366003306352640000, 15573012689517863187913236259514917169004544 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
In general, for k>=1, H(k*n,n) ~ exp(-k^2/4) * 2^(k*n) * n^(k*n).
LINKS
Eric Weisstein's World of Mathematics, Hermite Polynomial.
Wikipedia, Hermite polynomial.
FORMULA
a(n) ~ exp(-9/4) * 2^(3*n) * n^(3*n).
MAPLE
a:= n-> simplify(HermiteH(3*n, n)):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 07 2021
MATHEMATICA
Table[HermiteH[3*n, n], {n, 0, 12}]
PROG
(PARI) a(n) = polhermite(3*n, n); \\ Michel Marcus, Nov 07 2021
CROSSREFS
Sequence in context: A202685 A172893 A072725 * A176186 A332184 A221232
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Nov 07 2021
STATUS
approved

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Last modified February 28 17:13 EST 2024. Contains 370400 sequences. (Running on oeis4.)