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 A326856 #10 Jul 29 2019 02:58:41 %S A326856 1,1,0,0,0,24,144,0,0,40320,403200,0,0,479001600,8643317760, %T A326856 29059430400,0,20922789888000,475108274995200,1871463083212800,0, %U A326856 2432902008176640000,76354225980899328000,525098781423304704000,0,620448401733239439360000 %N A326856 E.g.f.: Product_{k>=1} (1 + x^(4*k-3) / (4*k-3)). %C A326856 In general, if c > 0, mod(d,c) <> 0 and e.g.f. = Product_{k>=1} (1 + x^(c*k+d) / (c*k+d)), then a(n) ~ n! * Gamma(1 + d/c) / (c^(1/c) * exp(gamma/c) * Gamma(1/c) * Gamma(1 + (d+1)/c) * n^(1 - 1/c)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function. %H A326856 Vaclav Kotesovec, <a href="/A326856/b326856.txt">Table of n, a(n) for n = 0..440</a> %H A326856 Vaclav Kotesovec, <a href="/A326856/a326856.jpg">Graph - the asymptotic ratio (40000 terms)</a> %F A326856 a(n) ~ n! / (sqrt(2*Pi) * exp(gamma/4) * n^(3/4)), where gamma is the Euler-Mascheroni constant A001620. %t A326856 nmax = 30; CoefficientList[Series[Product[(1+x^(4*k-3)/(4*k-3)), {k, 1, Floor[nmax/4]+1}], {x, 0, nmax}], x] * Range[0, nmax]! %Y A326856 Cf. A007838, A088994, A326780, A326855. %K A326856 nonn %O A326856 0,6 %A A326856 _Vaclav Kotesovec_, Jul 27 2019