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 A336976 #17 May 06 2021 06:53:37 %S A336976 1,1,3,7,15,32,65,131,260,501,965,1825,3419,6326,11652,21230,38405, %T A336976 69015,123334,218980,386809,679757,1189360,2071761,3594325,6211826, %U A336976 10698409,18363038,31420994,53605525,91198970,154746133,261929303,442310873,745264674,1253081340,2102754561 %N A336976 Expansion of Product_{k>=1} 1/(1 - x^k * (1 + k*x)). %H A336976 Seiichi Manyama, <a href="/A336976/b336976.txt">Table of n, a(n) for n = 0..1000</a> %F A336976 G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (1 + k/d * x)^d / d). %F A336976 a(n) ~ c * phi^(n+1) / sqrt(5), where c = Product_{k>=2} 1/(1 - 1/phi^k*(1 + k/phi)) = 167.5661037860673786430316975350024960626825333609486463342... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, May 06 2021 %t A336976 m = 36; CoefficientList[Series[Product[1/(1 - x^k*(1 + k*x)), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 01 2021 *) %o A336976 (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k*(1+k*x))) %o A336976 (PARI) N=66; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, (1+k/d*x)^d/d)))) %Y A336976 Cf. A227681, A336975, A336977, A336978, A336979, A336980. %K A336976 nonn %O A336976 0,3 %A A336976 _Seiichi Manyama_, Aug 09 2020