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A360817
Expansion of Sum_{k>=0} (k*x)^(3*k) / (1 - k*x)^(k+1).
2
1, 0, 0, 1, 2, 3, 68, 389, 1542, 24810, 251564, 1814487, 27520734, 391640548, 4295115396, 69305652406, 1221344986380, 18207710383335, 329699350020676, 6759819628538561, 126950556666301050, 2624697847966227077, 60825028694289947940, 1365568620213461601924
OFFSET
0,5
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/3)} k^n * binomial(n-2*k,k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^(3*k)/(1-k*x)^(k+1)))
(PARI) a(n) = sum(k=0, n\3, k^n*binomial(n-2*k, k));
CROSSREFS
Cf. A360815.
Sequence in context: A365504 A041249 A356795 * A184949 A132598 A257173
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved