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 A215890 #31 Aug 06 2016 13:34:36
%S A215890 1,7,461,84827,30648697,18319873199,16364889804485,20422587185959363,
%T A215890 33936856584735107441,72442485189323515166807,
%U A215890 193177550094285124372564285,629325007854898466696826469931,2459394825443160188158170494692841,11355850594904678701281528241280254207,61160283986030409241528644478489460162357,380011322281573634548774673447708463134715539
%N A215890 E.g.f.: Shw(x) / Chw(x), where Chw(x) = Sum_{n>=0} (2*n+1)^(2*n-1) * x^(2*n)/(2*n)! and Shw(x) = Sum_{n>=0} (2*n+2)^(2*n) * x^(2*n+1)/(2*n+1)!, with zero coefficients omitted.
%C A215890 It appears that terms are not divisible by 2 or 3.
%H A215890 Paul D. Hanna, <a href="/A215890/b215890.txt">Table of n, a(n) for n = 1..200</a>
%F A215890 E.g.f.: tanh(x*Chw(x)) = tanh( Sum_{n>=0} (2*n+1)^(2*n)*x^(2*n+1)/(2*n+1)! ).
%e A215890 E.g.f.: A(x) = x + 7*x^3/3! + 461*x^5/5! + 84827*x^7/7! + 30648697*x^9/9! +...
%e A215890 such that A(x) = Shw(x)/Chw(x) = tanh(x*Chw(x)) where
%e A215890 Shw(x) = x + 16*x^3/3! + 1296*x^5/5! + 262144*x^7/7! + 100000000*x^9/9! +...+ (2*n+2)^(2*n)*x^(2*n+1)/(2*n+1)! +...
%e A215890 Chw(x) = 1 + 3*x^2/2! + 125*x^4/4! + 16807*x^6/6! + 4782969*x^8/8! + 2357947691*x^10/10! +...+ (2*n+1)^(2*n-1)*x^(2*n)/(2*n)! +...
%e A215890 and Chw(x) + Shw(x) = LambertW(-x)/(-x).
%t A215890 max = 28; Chw[x_] := (-ProductLog[-x] + ProductLog[x])/(2*x); Shw[x_] := -(ProductLog[-x] + ProductLog[x])/(2*x); se = Series[ Shw[x]/Chw[x], {x, 0, max}]; (CoefficientList[se, x] // DeleteCases[#, 0] &)*Range[1, max, 2]! (* _Jean-François Alcover_, Jun 24 2013 *)
%o A215890 (PARI) {a(n)=local(Chw=sum(m=0, n, (2*m+1)^(2*m-1)*x^(2*m)/(2*m)!)+x*O(x^(2*n)),Shw=sum(m=0, n, (2*m+2)^(2*m)*x^(2*m+1)/(2*m+1)!)+x*O(x^(2*n+1))); (2*n+1)!*polcoeff(Shw/Chw, 2*n+1)}
%o A215890 for(n=0,20,print1(a(n),", "))
%o A215890 (PARI) {a(n)=(2*n+1)!*polcoeff( tanh( sum(m=0, n, (2*m+1)^(2*m)*x^(2*m+1)/(2*m+1)!) +x*O(x^(2*n+1))), 2*n+1)}
%o A215890 for(n=0,20,print1(a(n),", "))
%Y A215890 Cf. A215880, A215881, A215882, A216143.
%K A215890 nonn
%O A215890 1,2
%A A215890 _Paul D. Hanna_, Aug 25 2012