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 A342110 #20 May 25 2025 07:44:37
%S A342110 1,0,1,6,61,770,12160,228382,4989621,124262532,3475892685,
%T A342110 107901412520,3681266754660,136918473752216,5513911474915116,
%U A342110 239034083286873630,11098790133822288645,549539910028075555016,28903562131933534643851,1609321474965547356327246
%N A342110 a(n) = Sum_{k=0..n} Stirling2(n,k) * Stirling2(n,n-k).
%H A342110 G. C. Greubel, <a href="/A342110/b342110.txt">Table of n, a(n) for n = 0..350</a>
%F A342110 From _Vaclav Kotesovec_, Feb 28 2021, updated May 25 2025: (Start)
%F A342110 a(n) ~ c * d^n * (n-1)!, where
%F A342110 d = A238258 = -2 / (LambertW(-2*exp(-2)) * (2 + LambertW(-2*exp(-2)))) = 3.0882773047417401791158400820254382768364448971420138767247...
%F A342110 c = 1/(2*Pi*sqrt((1 + LambertW(-2*exp(-2)))*(3 + LambertW(-2*exp(-2))))) = 0.12826577250734152801558828593238744179869387423941684693208180123477... (End)
%t A342110 Table[Sum[StirlingS2[n, k]*StirlingS2[n, n-k], {k, 0, n}], {n, 0, 20}]
%o A342110 (PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*stirling(n, n-k, 2)); \\ _Michel Marcus_, Feb 28 2021
%o A342110 (Magma) [(&+[StirlingSecond(n, k)*StirlingSecond(n, n-k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jun 03 2021
%o A342110 (Sage) [sum( stirling_number2(n, k)*stirling_number2(n, n-k) for k in (0..n) ) for n in (0..30)] # _G. C. Greubel_, Jun 03 2021
%Y A342110 Cf. A008277, A014322, A047797, A342111.
%Y A342110 Cf. A048993.
%K A342110 nonn
%O A342110 0,4
%A A342110 _Vaclav Kotesovec_, Feb 28 2021