A346679 Expansion of Product_{k>=1} (1 + x^k*(1+x)) / (1 - x^k*(1+x)).

1, 2, 6, 14, 32, 68, 140, 280, 544, 1034, 1930, 3544, 6416, 11472, 20288, 35532, 61696, 106304, 181906, 309362, 523228, 880576, 1475424, 2462302, 4094682, 6787588, 11219504, 18498094, 30429502, 49955706, 81864400, 133940690, 218834842, 357090226, 582050680

Offset: 0

Author

Vaclav Kotesovec, Jul 31 2021

Keywords

• nonn

Comments

Convolution of A160571 and A227681.

Crossrefs

Cf. A160571, A227681.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k*(1+x))/(1-x^k*(1+x)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ 2*c * phi^(n+1) / sqrt(5), where phi = A001622 is the golden ratio and c = Product_{k>=2} (phi^k + 1 + 1/phi) / (phi^k - 1 - 1/phi) = 32.9911047431709572178149423384235021321790640826498395008790713974339...