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A352659
a(n) = n! * Sum_{k=0..floor(n/3)} 1 / (3*k)!.
4
1, 1, 2, 7, 28, 140, 841, 5887, 47096, 423865, 4238650, 46625150, 559501801, 7273523413, 101829327782, 1527439916731, 24439038667696, 415463657350832, 7478345832314977, 142088570813984563, 2841771416279691260, 59677199741873516461, 1312898394321217362142
OFFSET
0,3
LINKS
FORMULA
E.g.f.: (exp(x) + 2 * exp(-x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).
a(n) = floor(c * n!), where c = 1.16805831... = A143819.
MATHEMATICA
Table[n! Sum[1/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Exp[x] + 2 Exp[-x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) a(n) = n! * sum(k=0, n\3, 1/(3*k)!); \\ Michel Marcus, Mar 29 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 25 2022
STATUS
approved