A360795 Expansion of Sum_{k>0} x^k / (1 - (k * x)^k)^(k+1).

1, 3, 4, 17, 6, 211, 8, 1929, 7300, 22601, 12, 1724809, 14, 6703047, 223678576, 738787345, 18, 65630598229, 20, 2119646503661, 24448573943662, 3423809253371, 24, 21453113652593665, 12016296386718776, 4240253019018225, 8255251542208471048, 67251293544533119589, 30

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

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

If p is prime, a(p) = 1 + p.

Mathematica

a[n_] := DivisorSum[n, #^(n-#) * Binomial[# + n/# - 1, #] &]; Array[a, 30] (* Amiram Eldar, Aug 02 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)^(k+1)))
(PARI) a(n) = sumdiv(n, d, d^(n-d)*binomial(d+n/d-1, d));

Crossrefs

Cf. A360787, A360788.

Cf. A339481, A360794.

Sequence in context: A252606 A248240 A110983 * A100560 A025534 A082000

Adjacent sequences: A360792 A360793 A360794 * A360796 A360797 A360798

Keyword

nonn

Author

Seiichi Manyama, Feb 21 2023

Status

approved