A078938 Cube of lower triangular matrix of A056857 (successive equalities in set partitions of n).

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, 88563, 86457, 39186, 10815, 1995, 252, 21, 1, 681870, 708504, 345828, 104496, 21630, 3192, 336, 24, 1, 5597643, 6136830, 3188268

Offset: 0

Author

Paul D. Hanna, Dec 18 2002

Keywords

• nonn
• tabl

Comments

Cube of the matrix exp(P)/exp(1) given in A011971. - Gottfried Helms, 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, Nov 26 2008]

Examples

			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,
...
		

Crossrefs

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.

Programs

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, Apr 08 2007

Formula

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, 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.

Extensions

Entry revised by N. J. A. Sloane, Apr 25 2007