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 A129324 #16 Jul 11 2020 11:03:21
%S A129324 0,0,1,6,36,220,1410,9534,68040,511704,4046310,33560010,291244668,
%T A129324 2638581972,24901833866,244333004790,2487900487440,26245651191600,
%U A129324 286408960814862,3228529392965250,37544229610105220,449858650676764140
%N A129324 Third column of PE^2.
%C A129324 Base matrix is in A011971; second power is in A078937; third power is in A078938; fourth power is in A078939.
%F A129324 PE=exp(matpascal(5))/exp(1); A = PE^2; a(n)=A[n,3]; with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^2; a(n)=A[n,3].
%F A129324 E.g.f.: (x^2/2) * exp(2 * (exp(x) - 1)). - _Ilya Gutkovskiy_, Jul 11 2020
%p A129324 A056857 := proc(n,c) combinat[bell](n-1-c)*binomial(n-1,c) ; end: A078937 := proc(n,c) add( A056857(n,k)*A056857(k+1,c),k=0..n) ; end: A129324 := proc(n) A078937(n+1,2) ; end: seq(A129324(n),n=0..23) ; # _R. J. Mathar_, May 30 2008
%t A129324 A056857[n_, c_] := If[n <= c, 0, BellB[n - 1 - c] Binomial[n - 1, c]];
%t A129324 A078937[n_, c_] := Sum[A056857[n, k] A056857[k + 1, c], {k, 0, n}];
%t A129324 a[n_] := A078937[n + 1, 2];
%t A129324 a /@ Range[0, 21] (* _Jean-François Alcover_, Mar 24 2020, after _R. J. Mathar_ *)
%Y A129324 Cf. A056857, A078937, A078938, A078944, A078945, A000110.
%Y A129324 Cf. A078937, A078938, A129323, A129324, A129325, A027710.
%Y A129324 Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333.
%K A129324 nonn,easy
%O A129324 0,4
%A A129324 _Gottfried Helms_, Apr 08 2007
%E A129324 More terms from _R. J. Mathar_, May 30 2008