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 A182507 #18 Apr 13 2021 19:02:40
%S A182507 1,1,2,12,232,12848,1858464,663242944,562426769024,1103780804371200,
%T A182507 4916976475489286656,48986367134323580374016,
%U A182507 1078808700869188981508990976,52024935094126934151475827453952,5451309776848243787358722272838524928
%N A182507 G.f.: Sum_{n>=0} n! * 2^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + k*2^k*x).
%C A182507 Compare the g.f. to the identities:
%C A182507 (1) 1/(1-x) = Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 + k*x).
%C A182507 (2) 1+x = Sum_{n>=0} 2^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + 2^k*x).
%C A182507 First differs from A309615 at a(5) = 12848, A309615(5) = 19230. - _Gus Wiseman_, Aug 11 2019
%H A182507 Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, <a href="https://arxiv.org/abs/2012.13570">Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow</a>, arXiv:2012.13570 [math.CO], 2020.
%e A182507 G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 232*x^4 + 12848*x^5 + 1858464*x^6 +...
%e A182507 such that
%e A182507 A(x) = 1 + x/(1+2*x) + 2!*2^1*x^2/((1+1*2*x)*(1+2*4*x)) + 3!*2^3*x^3/((1+1*2*x)*(1+2*4*x)*(1+3*8*x)) + 4!*2^6*x^4/((1+1*2*x)*(1+2*4*x)*(1+3*8*x)*(1+4*16*x)) +...
%o A182507 (PARI) {a(n)=polcoeff(sum(m=0,n,m!*2^(m*(m-1)/2)*x^m/prod(k=1,m,1+k*2^k*x +x*O(x^n))),n)}
%o A182507 for(n=0,20,print1(a(n),", "))
%Y A182507 Cf. A005329, A182489, A309615.
%K A182507 nonn
%O A182507 0,3
%A A182507 _Paul D. Hanna_, May 03 2012