A110153 Expansion of g.f.: Product_{n>=1} 1/(1 - 3^n*x^n)^(3/3^n).

1, 3, 12, 39, 138, 426, 1461, 4458, 14655, 45309, 145479, 443037, 1427196, 4329696, 13655325, 41795679, 131102229, 397649811, 1247247507, 3775785681, 11761535064, 35770717695, 110693177805, 335003030301, 1040296817955, 3145674794979, 9695067728493, 29405519846121

Offset: 0

Author

Paul D. Hanna, Jul 14 2005

Keywords

• nonn

Examples

			A(x) = 1 + 3*x + 12*x^2 + 39*x^3 + 138*x^4 + 426*x^5 + ... =
  1/[(1-3*x)*(1-9*x^2)^(1/3)*(1-27*x^3)^(1/9)*(1-81*x^4)^(1/27)*...].
		

Crossrefs

Cf. A110152, A110154, A110155, A110156.

Programs

Mathematica

nmax=27; CoefficientList[Series[Product[1/(1 - 3^n*x^n)^(3/3^n),{n,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 21 2024 *)

PARI

a(n)=polcoeff(prod(k=1,n,1/(1-3^k*x^k+x*O(x^n))^(3/3^k)),n)

Extensions

a(25)-a(27) from Stefano Spezia, Jun 21 2024