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 A367152 #10 Nov 07 2023 08:56:39 %S A367152 1,1,7,101,2250,68184,2619822,122071704,6689791392,421670267136, %T A367152 30055781201520,2390512621714656,209893714832795760, %U A367152 20165895195283566000,2104433775967024226592,237043144515185017456320,28664975599576485530851584,3704019298858867019823244800 %N A367152 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3). %F A367152 a(n) = (3*n)! * Sum_{k=0..n} |Stirling1(n,k)|/(3*n-k+1)!. %F A367152 a(n) ~ (-3 - LambertW(-1, -3*exp(-4)))^(2*n+1) * (-LambertW(-1, -3*exp(-4)))^n * n^(n-1) / (sqrt(-3 - 3*LambertW(-1, -3*exp(-4))) * exp(n)). - _Vaclav Kotesovec_, Nov 07 2023 %t A367152 Table[(3*n)! * Sum[Abs[StirlingS1[n,k]]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 07 2023 *) %o A367152 (PARI) a(n) = (3*n)!*sum(k=0, n, abs(stirling(n, k, 1))/(3*n-k+1)!); %Y A367152 Cf. A138013, A367080. %K A367152 nonn %O A367152 0,3 %A A367152 _Seiichi Manyama_, Nov 07 2023