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 A299034 #8 Sep 08 2018 06:04:47 %S A299034 1,1,8,93,1544,32615,843264,25739539,906373376,36163950849, %T A299034 1612483625600,79458277381901,4288069172500992,251520785449249927, %U A299034 15932801526165085184,1084003570689331039875,78835487923639854792704,6103175938145968656408641,501114006272655771562911744 %N A299034 a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k)^(n/k). %H A299034 Vaclav Kotesovec, <a href="/A299034/b299034.txt">Table of n, a(n) for n = 0..300</a> %F A299034 a(n) = n! * [x^n] exp(n*Sum_{k>=1} d(k)*x^k/k), where d(k) is the number of divisors of k (A000005). %F A299034 a(n) ~ c * d^n * n^n, where d = 1.7257974131308983723949107467... and c = 0.693704376971941705824592525... - _Vaclav Kotesovec_, Sep 08 2018 %e A299034 The table of coefficients of x^k in expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(n/k) begins: %e A299034 n = 0: (1), 0, 0, 0, 0, 0, 0, ... %e A299034 n = 1: 1, (1), 3, 11, 59, 339, 2629, ... %e A299034 n = 2: 1, 2, (8), 40, 260, 1928, 17056, ... %e A299034 n = 3: 1, 3, 15, (93), 711, 6237, 62901, ... %e A299034 n = 4: 1, 4, 24, 176, (1544), 15456, 174784, ... %e A299034 n = 5: 1, 5, 35, 295, 2915, (32615), 407725, ... %e A299034 n = 6: 1, 6, 48, 456, 5004, 61704, (843264), ... %t A299034 Table[n! SeriesCoefficient[Product[1/(1 - x^k)^(n/k), {k, 1, n}], {x, 0, n}], {n, 0, 18}] %Y A299034 Cf. A000005, A028342, A255672, A299033. %K A299034 nonn %O A299034 0,3 %A A299034 _Ilya Gutkovskiy_, Feb 01 2018