A265951 Expansion of Product_{k>=1} 1/(1 - 2*k*x^k).

1, 2, 8, 22, 68, 170, 484, 1166, 3048, 7274, 18000, 41806, 100684, 229258, 535692, 1206230, 2758944, 6123650, 13798088, 30284894, 67272756, 146426002, 321513284, 693944814, 1510245960, 3236648578, 6985572672, 14885926182, 31904642348, 67618415690

Offset: 0

Author

Vaclav Kotesovec, Dec 19 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..3280

Crossrefs

Cf. A006906, A265974, A265975, A265976.

Cf. A032309, A070933, A265955.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      2^n, b(n, i-1) +i*2*b(n-i, min(n-i, i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..32);  # Alois P. Heinz, Aug 23 2019

Mathematica

nmax=40; CoefficientList[Series[Product[1/(1-2*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * n * 2^n, where c = 1/2 * Product_{m>=3} 1/(1 - m/2^(m-1)) = 9.281573281805057363737677116134642024212942973614535341005126953773818...