0,2

Cube of the matrix exp(P)/exp(1) given in A011971. - Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007. Base matrix in A011971, second power in A129321, third power in this entry, fourth power in A078939

First column gives A027710. Row sums give A078940.

Riordan array [exp(3*exp(x)-3),x], whose production matrix has e.g.f. exp(x*t)(t+3*exp(x)). [From Paul Barry (pbarry(AT)wit.ie), Nov 26 2008]

PE=exp(matpascal(5))/exp(1); A = PE^3; a(n)= A[ n,sequentially read ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^3; a(n)=A[ n,sequentially read] - Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007

Exponential function of 3*Pascal's triangle (taken as a lower triangular matrix) divided by e^3: [A078938] = (1/e^3)*exp(3*[A007318]) = [A056857]^3.

Rows: {1}, {3,1}, {12,6,1}, {57,36,9,1}, {309,228,72,12,1}, {1866,1545,570,120,15,1}, {12351,11196,4635,1140,180,18,1}, ...

(PARI) m=matpascal(5)-matid(6); pe=matid(6)+m/1! + m^2/2!+m^3/3!+m^4/4!+m^5/5! ; A = pe^3 - Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007

Cf. A056857, A078937, A078939, A078940, A027710.

Cf. A078938, A078944, A078945, A000110.

Cf. A129321, A129323, A129324, A129325, A027710.

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

Sequence in context: A113369 A127894 A127898 this_sequence A135888 A133366 A049458

Adjacent sequences: A078935 A078936 A078937 this_sequence A078939 A078940 A078941

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 18 2002

Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 25 2007