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 A360239 #10 Feb 13 2023 03:41:48
%S A360239 1,2,23,502,16414,716936,39167817,2567058766,196159319943,
%T A360239 17118727499178,1679643875717867,183020512751712554,
%U A360239 21928106267349661127,2865208654370111795940,405479888251812823615679,61785441098476295018209264,10085622916281496742096639996
%N A360239 G.f. A(x) = exp( Sum_{k>=1} A360238(k) * x^k/k ), where A360238(k) = [y^k*x^k/k] log( Sum_{m>=0} (m + y)^(2*m) * x^m ) for k >= 1.
%C A360239 Related series: C(x)^2 = exp( Sum_{k>=1} A000984(k) * x^k/k ), where C(x) = 1 + x*C(x)^2 is the Catalan function and A000984(k) = [y^k*x^k/k] log( Sum_{m>=0} (1 + y)^(2*m) * x^m ) for k >= 1.
%H A360239 Paul D. Hanna, <a href="/A360239/b360239.txt">Table of n, a(n) for n = 0..200</a>
%F A360239 a(n) ~ (1 - exp(-1)/4) * 2^(2*n) * n^(n - 1/2) / sqrt(Pi). - _Vaclav Kotesovec_, Feb 12 2023
%e A360239 G.f.: A(x) = 1 + 2*x + 23*x^2 + 502*x^3 + 16414*x^4 + 716936*x^5 + 39167817*x^6 + 2567058766*x^7 + 196159319943*x^8 + 17118727499178*x^9 + ...
%e A360239 such that
%e A360239 log(A(x)) = 2*x + 42*x^2/2 + 1376*x^3/3 + 60934*x^4/4 + 3377252*x^5/5 + 224036904*x^6/6 + 17282039280*x^7/7 + ... + A360238(n)*x^n/n + ...
%e A360239 where A360238(n) equals the coefficient of y^n*x^n/n in the logarithmic series:
%e A360239 log( Sum_{m>=0} (m + y)^(2*m) * x^m ) = (y^2 + 2*y + 1)*x + (y^4 + 12*y^3 + 42*y^2 + 60*y + 31)*x^2/2 + (y^6 + 30*y^5 + 297*y^4 + 1376*y^3 + 3348*y^2 + 4188*y + 2140)*x^3/3 + (y^8 + 56*y^7 + 1100*y^6 + 10792*y^5 + 60934*y^4 + 209464*y^3 + 436692*y^2 + 510952*y + 258779)*x^4/4 + (y^10 + 90*y^9 + 2945*y^8 + 49960*y^7 + 510160*y^6 + 3377252*y^5 + 14971780*y^4 + 44457000*y^3 + 85336175*y^2 + 96141170*y + 48446971)*x^5/5 + ...
%o A360239 (PARI) {A360238(n) = n * polcoeff( polcoeff( log( sum(m=0, n+1, (m + y)^(2*m) *x^m ) +x*O(x^n) ), n, x), n, y)}
%o A360239 {a(n) = polcoeff( exp( sum(m=1,n, A360238(m)*x^m/m ) +x*O(x^n)),n)}
%o A360239 for(n=0,20,print1(a(n),", "))
%Y A360239 Cf. A360238, A360349, A000108, A000984.
%K A360239 nonn
%O A360239 0,2
%A A360239 _Paul D. Hanna_, Feb 11 2023