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A360728
Expansion of Sum_{k>=0} (k * x * (1 + x^3))^k.
4
1, 1, 4, 27, 257, 3133, 46737, 824567, 16792845, 387700506, 10005766337, 285445919589, 8919587932524, 302975123887680, 11115145723728035, 438000897534309171, 18450681900124075166, 827395845674975999727, 39352977072147424071861
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/4)} (n-3*k)^(n-3*k) * binomial(n-3*k,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+x^3))^k))
(PARI) a(n) = sum(k=0, n\4, (n-3*k)^(n-3*k)*binomial(n-3*k, k));
CROSSREFS
Cf. A360731.
Sequence in context: A240582 A338693 A360776 * A353014 A360731 A328694
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2023
STATUS
approved