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 A129332 #10 Mar 24 2020 08:03:58
%S A129332 0,0,1,12,120,1160,11340,113988,1185968,12802896,143475300,1668342060,
%T A129332 20111265768,251047344600,3241258872124,43230289541460,
%U A129332 594927620980320,8438127851537312,123214473695309652,1850390947982126268
%N A129332 Third column of PE^4.
%C A129332 Base matrix is in A011971; second power is in A078937; third power is in A078938; fourth power is in A078939.
%F A129332 PE=exp(matpascal(5))/exp(1); A = PE^4; a(n)= A[ n,3 ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^4; a(n)=A[ n,3]
%p A129332 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: A078938 := proc(n,c) add( A078937(n,k)*A056857(k+1,c),k=0..n) ; end: A078939 := proc(n,c) add( A078938(n,k)*A056857(k+1,c),k=0..n) ; end: A129332 := proc(n) A078939(n+1,2) ; end: seq(A129332(n),n=0..25) ; # _R. J. Mathar_, May 30 2008
%t A129332 A056857[n_, c_] := If[n <= c, 0, BellB[n - 1 - c] Binomial[n - 1, c]];
%t A129332 A078937[n_, c_] := Sum[A056857[n, k] A056857[k + 1, c], {k, 0, n}];
%t A129332 A078938[n_, c_] := Sum[A078937[n, k] A056857[k + 1, c], {k, 0, n}];
%t A129332 A078939[n_, c_] := Sum[A078938[n, k] A056857[k + 1, c], {k, 0, n}];
%t A129332 a[n_] := A078939[n + 1, 2];
%t A129332 a /@ Range[0, 19] (* _Jean-François Alcover_, Mar 24 2020, after _R. J. Mathar_ *)
%Y A129332 Cf. A056857, A078937, A078938, A078944, A078945, A000110.
%Y A129332 Cf. A078937, A078938, A129323, A129324, A129325, A027710.
%Y A129332 Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333.
%K A129332 nonn,easy
%O A129332 0,4
%A A129332 _Gottfried Helms_, Apr 08 2007
%E A129332 More terms from _R. J. Mathar_, May 30 2008