This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370739 #8 Feb 29 2024 06:23:20
%S A370739 1,15,-75,35250,-1138125,72645000,-3307996875,244578890625,
%T A370739 -15502648125000,985908809765625,-63515254624218750,
%U A370739 4314500023927734375,-291905297026816406250,19789483493484814453125,-1355414138248614990234375,93666904586649390380859375,-6498800175020013123779296875
%N A370739 a(n) = 5^(2*n) * [x^n] Product_{k>=1} (1 + 3*x^k)^(1/5).
%C A370739 In general, if d > 1, m > 1 and g.f. = Product_{k>=1} (1 + d*x^k)^(1/m), then a(n) ~ (-1)^(n+1) * QPochhammer(-1/d)^(1/m) * d^n / (m*Gamma(1 - 1/m) * n^(1 + 1/m)).
%F A370739 G.f.: Product_{k>=1} (1 + 3*(25*x)^k)^(1/5).
%F A370739 a(n) ~ (-1)^(n+1) * QPochhammer(-1/3)^(1/5) * 75^n / (5 * Gamma(4/5) * n^(6/5)).
%t A370739 nmax = 20; CoefficientList[Series[Product[1+3*x^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
%t A370739 nmax = 20; CoefficientList[Series[Product[1+3*(25*x)^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]
%Y A370739 Cf. A032308 (d=3,m=1), A370711 (d=3,m=2), A370712 (d=3,m=3), A370738 (d=3,m=4).
%Y A370739 Cf. A032302 (d=2,m=1), A370709 (d=2,m=2), A370716 (d=2,m=3), A370736 (d=2,m=4), A370737 (d=2,m=5).
%Y A370739 Cf. A000009 (d=1,m=1), A298994 (d=1,m=2), A303074 (d=1,m=3)
%K A370739 sign
%O A370739 0,2
%A A370739 _Vaclav Kotesovec_, Feb 28 2024