A327798 Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*(j + 1))).

1, 0, 1, 1, 3, 3, 9, 10, 25, 34, 72, 106, 215, 330, 635, 1025, 1899, 3141, 5713, 9602, 17213, 29292, 51982, 89149, 157249, 271027, 476037, 823386, 1442063, 2500015, 4370386, 7588146, 13248591, 23026728, 40169991, 69865026, 121811765, 211954826, 369412910

Offset

0,5

Comments

Invert transform of A032741.

Links

Robert Israel, Table of n, a(n) for n = 0..3000

Formula

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

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

Maple

N:= 100: # for a(0)..a(N)
G:= 1/(1-add(x^(2*k)/(1-x^k), k=1..(N+1)/2)):
S:= series(G, x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, Jan 10 2023

Mathematica

nmax = 38; CoefficientList[Series[1/(1 - Sum[x^(2 k)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(DivisorSigma[0, k] - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 38}]

Crossrefs

Cf. A032741, A129921, A318783, A327739.

Sequence in context: A223743 A117783 A121445 * A121074 A121072 A133164

Adjacent sequences: A327795 A327796 A327797 * A327799 A327800 A327801

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 25 2019

Status

approved