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 A380212 #13 Jan 23 2025 05:43:11
%S A380212 1,3,24,267,3771,64188,1273599,28784997,728619516,20389690953,
%T A380212 624380711769,20749726230192,743217114278241,28526465892902643,
%U A380212 1167521852585583504,50735768950040355747,2332267950561718237011,113040281313704744222148,5759890462485002871029439
%N A380212 Expansion of e.g.f. exp( 1/(1-2*x)^(3/2) - 1 ).
%F A380212 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * |Stirling1(n,k)| * Bell(k).
%F A380212 a(n) = (1/e) * (-2)^n * n! * Sum_{k>=0} binomial(-3*k/2,n)/k!.
%F A380212 a(n) ~ 3^(1/5) * 5^(-1/2) * 2^(n + 3/10) * n^(n - 1/5) * exp(-1 + 2^(1/5)*3^(4/5)*n^(1/5)/4 + 5*2^(3/5)*3^(2/5)*n^(3/5)/6 - n) * (1 + 2^(4/5)*3^(1/5)/(10*n^(1/5))). - _Vaclav Kotesovec_, Jan 23 2025
%t A380212 Table[Sum[3^k * 2^(n-k) * Abs[StirlingS1[n,k]] * BellB[k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 23 2025 *)
%o A380212 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1/(1-2*x)^(3/2)-1)))
%Y A380212 Cf. A049118, A380213.
%K A380212 nonn
%O A380212 0,2
%A A380212 _Seiichi Manyama_, Jan 16 2025