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A360733
Expansion of Sum_{k>0} (x * (1 + (k * x)^k))^k.
2
1, 2, 1, 9, 1, 98, 1, 1025, 2188, 15626, 1, 692836, 1, 5764802, 97656251, 201326593, 1, 36138519442, 1, 409470748547, 14242684529830, 3138428376722, 1, 10019491686645761, 476837158203126, 3937376385699290, 5403406870691968357, 19704673338472752470, 1
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} d^(n-d) * binomial(d,n/d-1).
If p is an odd prime, a(p) = 1.
MATHEMATICA
a[n_] := DivisorSum[n, #^(n-#) * Binomial[#, n/# - 1] &]; Array[a, 30] (* Amiram Eldar, Aug 09 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (x*(1+(k*x)^k))^k))
(PARI) a(n) = sumdiv(n, d, d^(n-d)*binomial(d, n/d-1));
CROSSREFS
Sequence in context: A133399 A128751 A129168 * A353204 A293416 A194555
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2023
STATUS
approved