A129327 Second column of PE^3.

0, 1, 6, 36, 228, 1545, 11196, 86457, 708504, 6136830, 55976430, 535904259, 5369146272, 56145107577, 611336534802, 6916529431620, 81152874393168, 985767316792449, 12376996566040980, 160399065135692073

Offset: 0

Author

Gottfried Helms, Apr 08 2007

Keywords

• nonn
• easy

Comments

Base matrix is in A011971; second power is in A078937; third power is in A078938; fourth power is in A078939.

Crossrefs

Cf. A056857, A078937, A078938, A078944, A078945, A000110.

Cf. A078937, A078938, A129323, A129324, A129325, A027710.

Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333.

Programs

Maple

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

Mathematica

Table[Sum[BellB[n, 3], {i, 0, n}], {n, -1, 18}] (* Zerinvary Lajos, Jul 16 2009 *)

Formula

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]

Extensions

More terms from R. J. Mathar, May 30 2008