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Second column of PE^4.
14

%I #9 Aug 18 2015 00:31:49

%S 0,1,8,60,464,3780,32568,296492,2845088,28695060,303334920,3351877628,

%T 38622668400,463036981732,5764038605528,74365952622540,

%U 992720923710272,13690497077256628,194777994524434344,2855149354656290716

%N Second column of PE^4.

%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^4; a(n)= A[ n,2 ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^4; 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: A078939 := proc(n,c) add( A078938(n,k)*A056857(k+1,c),k=0..n) ; end: A129331 := proc(n) A078939(n+1,1) ; end: seq(A129331(n),n=0..25) ; # _R. J. Mathar_, May 30 2008

%t Table[Sum[BellB[n, 4], {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