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A373743
Expansion of e.g.f. exp(x^3/6 * (1 + x)^2).
0
1, 0, 0, 1, 8, 20, 10, 280, 3360, 20440, 67200, 462000, 7407400, 73673600, 482081600, 3364761400, 47311264000, 657536880000, 6586994814400, 58707179731200, 740032028736000, 11832726841936000, 161121297104768000, 1857897194273120000, 23875495204536976000
OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(2*k,n-3*k)/(6^k * k!).
a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 8*(n-3)*a(n-4) + 5*(n-3)*(n-4)*a(n-5)).
PROG
(PARI) a(n) = n!*sum(k=0, n\3, binomial(2*k, n-3*k)/(6^k*k!));
CROSSREFS
Cf. A264622.
Sequence in context: A120081 A173206 A288423 * A081963 A208085 A334065
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 16 2024
STATUS
approved