A327764 Expansion of 1 / (1 - Sum_{i>=1, j>=1} x^(i*j*(j + 1)/2)).

1, 1, 2, 5, 10, 21, 47, 99, 211, 455, 973, 2081, 4464, 9558, 20466, 43848, 93914, 201140, 430844, 922818, 1976553, 4233613, 9067960, 19422576, 41601229, 89105550, 190854784, 408791400, 875589076, 1875421302, 4016959325, 8603912899, 18428694036, 39472363286

Offset

0,3

Comments

Invert transform of A007862.

Links

Table of n, a(n) for n=0..33.

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A007862(k) * a(n-k).

Mathematica

nmax = 33; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2)/(1 - x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Length[Select[Divisors[k], IntegerQ[Sqrt[8 # + 1]] &]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]

Crossrefs

Cf. A007862, A129921, A327738, A327744, A327745.

Sequence in context: A247594 A209469 A208275 * A192317 A361779 A360748

Adjacent sequences: A327761 A327762 A327763 * A327765 A327766 A327767

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 24 2019

Status

approved