A280088 Expansion of Product_{k>=1} 1/(1 - x^k)^(k!!).

1, 1, 3, 6, 17, 38, 112, 280, 882, 2416, 8253, 24458, 91051, 289704, 1172288, 3980034, 17413820, 62706119, 294608079, 1118820630, 5603910081, 22328924231, 118432939871, 492897768426, 2752203529333, 11918139966134, 69709167028426, 313080284080648, 1910245872252972, 8873669214476627, 56283324138424814, 269790676411694902

Offset: 0

Author

Ilya Gutkovskiy, Dec 25 2016

Keywords

• nonn

Comments

Euler transform of the double factorials (A006882).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A006882, A107895.

Programs

Mathematica

nmax = 31; CoefficientList[Series[Product[1/(1 - x^k)^(k!!), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^k)^(k!!).

a(n) ~ n!!. - Vaclav Kotesovec, Dec 25 2016