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

0,2

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]

Links

Table of n, a(n) for n=0..47.

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.

Example

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,
...

Prog

(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

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.

Sequence in context: A201638 A127894 A127898 * A135888 A329433 A258245

Adjacent sequences: A078935 A078936 A078937 * A078939 A078940 A078941

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 18 2002

Extensions

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

Status

approved