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A361533
Expansion of e.g.f. exp(x^3/(6 * (1-x))).
6
1, 0, 0, 1, 4, 20, 130, 980, 8400, 80920, 865200, 10164000, 130114600, 1802600800, 26867640800, 428661633400, 7288513232000, 131558835408000, 2512282795422400, 50600743739145600, 1071998968264224000, 23829055696093648000, 554524256514356128000
OFFSET
0,5
FORMULA
a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + binomial(n-1,2) * a(n-3) - 2*binomial(n-1,3) * a(n-4) for n > 3.
a(n) ~ 2^(-3/4) * 3^(-1/4) * exp(-5/12 + sqrt(2*n/3) - n) * n^(n - 1/4). - Vaclav Kotesovec, Mar 29 2023
From Seiichi Manyama, Jun 17 2024: (Start)
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k-1,n-3*k)/(6^k * k!).
a(0) = 1; a(n) = ((n-1)!/6) * Sum_{k=3..n} k * a(n-k)/(n-k)!. (End)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3/(6*(1-x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 15 2023
STATUS
approved