A320650 Expansion of 1/(1 - Sum_{k>=1} x^k/(1 - x^(2*k))).

1, 1, 2, 5, 10, 22, 48, 103, 222, 481, 1038, 2241, 4842, 10456, 22582, 48776, 105342, 227514, 491386, 1061281, 2292132, 4950510, 10692006, 23092378, 49874474, 107717891, 232646956, 502466304, 1085216744, 2343829586, 5062156694, 10933145610, 23613191032

Offset

0,3

Comments

Invert transform of A001227.

Links

Robert Israel, Table of n, a(n) for n = 0..2986

N. J. A. Sloane, Transforms

Formula

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

G.f.: 1/(1 + x * (d/dx) log(Product_{k>=1} (1 - x^(2*k-1))^(1/(2*k-1)))).

a(0) = 1; a(n) = Sum_{k=1..n} A001227(k)*a(n-k).

Maple

a:=series(1/(1-add(x^k/(1-x^(2*k)), k=1..100)), x=0, 33): seq(coeff(a, x, n), n=0..32); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 32; CoefficientList[Series[1/(1 - Sum[x^k/(1 - x^(2 k)), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 32; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[Mod[d, 2], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 32}]

Crossrefs

Cf. A001227, A129921, A206303.

Sequence in context: A124329 A144520 A101399 * A018109 A341020 A123491

Adjacent sequences: A320647 A320648 A320649 * A320651 A320652 A320653

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 18 2018

Status

approved