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A356328
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a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * (n - 3*k)!).
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3
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1, 1, 1, 1, 5, 21, 61, 281, 2521, 15625, 84841, 971521, 10646461, 83366141, 962405445, 15445935961, 181502928881, 2182235585041, 42297481449361, 714940186390465, 10007476059187381, 204722588272279141, 4600003555996715021, 80767827313930590681
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^3/6)).
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MATHEMATICA
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a[n_] := n! * Sum[(n - 3*k)^k/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 24, 0] (* Amiram Eldar, Aug 19 2022 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*(n-3*k)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^3/6)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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