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 A192989 #27 Sep 08 2022 08:45:58
%S A192989 1,3,15,87,585,4383,35919,318195,3015441,30354075,322626159,
%T A192989 3603292047,42120047385,513557128503,6512375759535,85673471945067,
%U A192989 1166675225150241,16413589529042355,238151194659626319,3558129109803374535
%N A192989 Expansion of e.g.f.: exp((1+x)^3 - 1).
%H A192989 Seiichi Manyama, <a href="/A192989/b192989.txt">Table of n, a(n) for n = 0..561</a>
%F A192989 a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(k) * 3^k.
%F A192989 Conjecture: a(n) -3*a(n-1) +6*(-n+1)*a(n-2) -3*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, May 12 2014
%F A192989 Remark: the above conjectured recurrence is true and can be easily obtained from the e.g.f. - _Emanuele Munarini_, Aug 31 2017
%F A192989 a(n) ~ 3^(n/3-1/2) * exp(-2*n/3 + 3^(1/3)*n^(2/3) + 3^(-1/3)*n^(1/3) - 2/3) * n^(2*n/3) * (1 + 23/(54*(n/3)^(1/3)) + 3149/(29160*(n/3)^(2/3))). - _Vaclav Kotesovec_, Jul 15 2014
%e A192989 E.g.f.: A(x) = 1 + 3*x + 15*x^2/2! + 87*x^3/3! + 585*x^4/4! +...
%t A192989 CoefficientList[Series[E^((1+x)^3-1), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jul 15 2014 *)
%t A192989 Table[Sum[ (-1)^(n - k) Abs[StirlingS1[n, k]] 3^k BellB[k], {k, 0, n}], {n, 0, 20}] (* _Emanuele Munarini_, Aug 31 2017 *)
%o A192989 (PARI) {a(n)=if(n<0, 0, n!*polcoeff(exp((1+x)^3-1+x*O(x^n)), n))}
%o A192989 (PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
%o A192989 {Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}
%o A192989 {a(n)=sum(k=0, n, Stirling1(n, k)*Bell(k)*3^k)}
%o A192989 (Maxima)
%o A192989 a(n) := sum((-1)^(n-k)*abs(stirling1(n,k))*3^k*belln(k),k,0,n);
%o A192989 makelist(a(n),n,0,12); /* _Emanuele Munarini_, Aug 31 2017 */
%o A192989 (Magma) [(&+[3^k*Bell(k)*StirlingFirst(n,k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Jul 25 2019
%o A192989 (Sage) [sum((-1)^(n-k)*3^k*bell_number(k)*stirling_number1(n,k) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Jul 25 2019
%o A192989 (GAP) List([0..20], n-> Sum([0..n], k-> (-1)^(n-k)*3^k*Bell(k)* Stirling1(n,k) )); # _G. C. Greubel_, Jul 25 2019
%Y A192989 Cf. A000110, A000898, A008275.
%K A192989 nonn
%O A192989 0,2
%A A192989 _Paul D. Hanna_, Jul 13 2011