This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339481 #18 Apr 25 2021 02:22:50 %S A339481 1,2,2,10,2,131,2,1282,4376,16907,2,1138272,2,5793475,154455992, %T A339481 469893122,2,49501130330,2,1318441711177,19001093813466,3138439911059, %U A339481 2,15989399214596398,6675720214843752,3937376603803099,6754271297694102092,47097064577536888014,2 %N A339481 a(n) = Sum_{d|n} d^(n-d) * binomial(d+n/d-2, d-1). %F A339481 G.f.: Sum_{k >= 1} (x/(1 - (k * x)^k))^k. %F A339481 If p is prime, a(p) = 2. %t A339481 a[n_] := DivisorSum[n, #^(n - #) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* _Amiram Eldar_, Apr 25 2021 *) %o A339481 (PARI) a(n) = sumdiv(n, d, d^(n-d)*binomial(d+n/d-2, d-1)); %o A339481 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-(k*x)^k))^k)) %Y A339481 Cf. A157019, A157020, A324158, A324159, A338661, A339482, A339712, A343573. %K A339481 nonn %O A339481 1,2 %A A339481 _Seiichi Manyama_, Apr 24 2021