A327736 Expansion of 1 / (1 - Sum_{i>=1, j>=0} x^(i*2^j)).

1, 1, 3, 6, 16, 35, 85, 195, 465, 1081, 2549, 5962, 14016, 32847, 77119, 180866, 424466, 995753, 2336497, 5481712, 12861904, 30176671, 70802913, 166120289, 389761751, 914476925, 2145596677, 5034105820, 11811287658, 27712248159, 65019931641, 152553127471, 357928110743

Offset

0,3

Comments

Invert transform of A001511.

Links

Table of n, a(n) for n=0..32.

Formula

G.f.: 1 / (1 - Sum_{k>=0} x^(2^k) / (1 - x^(2^k))).

a(0) = 1; a(n) = Sum_{k=1..n} A001511(k) * a(n-k).

Mathematica

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

Crossrefs

Cf. A000041, A001511, A092119, A129921.

Sequence in context: A053305 A049311 A068590 * A319752 A130095 A293993

Adjacent sequences: A327733 A327734 A327735 * A327737 A327738 A327739

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2019

Status

approved