A360733 Expansion of Sum_{k>0} (x * (1 + (k * x)^k))^k.

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

Author

Seiichi Manyama, Feb 18 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 1..599

Crossrefs

Cf. A327249, A360732.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(n-#) * Binomial[#, n/# - 1] &]; Array[a, 30] (* Amiram Eldar, Aug 09 2023 *)

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));

Formula

a(n) = Sum_{d|n} d^(n-d) * binomial(d,n/d-1).

If p is an odd prime, a(p) = 1.