Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Aug 09 2023 00:51:47
%S 1,2,1,9,1,98,1,1025,2188,15626,1,692836,1,5764802,97656251,201326593,
%T 1,36138519442,1,409470748547,14242684529830,3138428376722,1,
%U 10019491686645761,476837158203126,3937376385699290,5403406870691968357,19704673338472752470,1
%N Expansion of Sum_{k>0} (x * (1 + (k * x)^k))^k.
%H Winston de Greef, <a href="/A360733/b360733.txt">Table of n, a(n) for n = 1..599</a>
%F a(n) = Sum_{d|n} d^(n-d) * binomial(d,n/d-1).
%F If p is an odd prime, a(p) = 1.
%t a[n_] := DivisorSum[n, #^(n-#) * Binomial[#, n/# - 1] &]; Array[a, 30] (* _Amiram Eldar_, Aug 09 2023 *)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (x*(1+(k*x)^k))^k))
%o (PARI) a(n) = sumdiv(n, d, d^(n-d)*binomial(d, n/d-1));
%Y Cf. A327249, A360732.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Feb 18 2023