A327798 - OEIS

%I #8 Jan 11 2023 07:47:25

%S 1,0,1,1,3,3,9,10,25,34,72,106,215,330,635,1025,1899,3141,5713,9602,

%T 17213,29292,51982,89149,157249,271027,476037,823386,1442063,2500015,

%U 4370386,7588146,13248591,23026728,40169991,69865026,121811765,211954826,369412910

%N Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*(j + 1))).

%C Invert transform of A032741.

%H Robert Israel, <a href="/A327798/b327798.txt">Table of n, a(n) for n = 0..3000</a>

%F G.f.: 1 / (1 - Sum_{k>=1} x^(2*k) / (1 - x^k)).

%F a(0) = 1; a(n) = Sum_{k=1..n} A032741(k) * a(n-k).

%p N:= 100: # for a(0)..a(N)

%p G:= 1/(1-add(x^(2*k)/(1-x^k),k=1..(N+1)/2)):

%p S:= series(G,x,N+1):

%p seq(coeff(S,x,i),i=0..N); # _Robert Israel_, Jan 10 2023

%t nmax = 38; CoefficientList[Series[1/(1 - Sum[x^(2 k)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = Sum[(DivisorSigma[0, k] - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 38}]

%Y Cf. A032741, A129921, A318783, A327739.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Sep 25 2019