A370737 a(n) = 5^(2*n) * [x^n] Product_{k>=1} (1 + 2*x^k)^(1/5).

1, 10, 50, 14750, -166250, 14011250, -133418750, 18136968750, -620089531250, 29520532031250, -917207280468750, 51260806902343750, -2257145499863281250, 101035630688769531250, -4434459153208496093750, 214279556679692871093750, -9859289197933918457031250, 454976266920750451660156250

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• sign

Crossrefs

Cf. A032302 (m=1), A370709 (m=2), A370716 (m=3), A370736 (m=4).

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1+2*x^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1+2*(25*x)^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + 2*(25*x)^k)^(1/5).

a(n) ~ (-1)^(n+1) * QPochhammer(-1/2)^(1/5) * 50^n / (5 * Gamma(4/5) * n^(6/5)).