%I #9 Aug 18 2015 00:26:53
%S 0,1,6,36,228,1545,11196,86457,708504,6136830,55976430,535904259,
%T 5369146272,56145107577,611336534802,6916529431620,81152874393168,
%U 985767316792449,12376996566040980,160399065135692073
%N Second column of PE^3.
%C Base matrix is in A011971; second power is in A078937; third power is in A078938; fourth power is in A078939.
%F PE=exp(matpascal(5))/exp(1); A = PE^3; a(n)= A[ n,2 ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^3; a(n)=A[ n,2]
%p 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: A129327 := proc(n) A078938(n+1,1) ; end: seq(A129327(n),n=0..27) ; # _R. J. Mathar_, May 30 2008
%t Table[Sum[BellB[n, 3], {i, 0, n}], {n, -1, 18}] (* _Zerinvary Lajos_, Jul 16 2009 *)
%Y Cf. A056857, A078937, A078938, A078944, A078945, A000110.
%Y Cf. A078937, A078938, A129323, A129324, A129325, A027710.
%Y Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333.
%K nonn,easy
%O 0,3
%A _Gottfried Helms_, Apr 08 2007
%E More terms from _R. J. Mathar_, May 30 2008