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URL: https://oeis.org/A360819

⇱ A360819 - OEIS

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A360819
Expansion of Sum_{k>=0} ( (k*x)^3 / (1 - k*x) )^k.
1
1, 0, 0, 1, 1, 1, 65, 257, 769, 21732, 182268, 1075171, 22120299, 292415838, 2784944366, 52394511682, 914813711338, 12411977351379, 240868108545883, 5024364548461861, 88977315031536205, 1888119425325238979, 44744897995532996819, 971263427084750362992
OFFSET
0,7
FORMULA
a(n) = Sum_{k=0..floor(n/3)} k^n * binomial(n-2*k-1,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, ((k*x)^3/(1-k*x))^k))
(PARI) a(n) = sum(k=0, n\3, k^n*binomial(n-2*k-1, n-3*k));
CROSSREFS
Cf. A360709.
Sequence in context: A038637 A158686 A115342 * A036547 A031694 A152023
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved