A111549 Matrix logarithm of triangle A111544.

0, 1, 0, 4, 2, 0, 23, 6, 3, 0, 165, 32, 9, 4, 0, 1383, 222, 47, 13, 5, 0, 13083, 1824, 321, 70, 18, 6, 0, 136863, 17016, 2607, 486, 103, 24, 7, 0, 1562715, 176112, 24099, 3990, 747, 148, 31, 8, 0, 19301319, 1993392, 247527, 37182, 6351, 1140, 207, 39, 9, 0

Offset: 0

Author

Paul D. Hanna, Aug 07 2005

Keywords

• nonn
• tabl

Comments

Column 0 (A111546) is found in column 3 of triangle A111544.

Examples

			Triangle begins:
0;
1,0;
4,2,0;
23,6,3,0;
165,32,9,4,0;
1383,222,47,13,5,0;
13083,1824,321,70,18,6,0;
136863,17016,2607,486,103,24,7,0;
1562715,176112,24099,3990,747,148,31,8,0; ...
		

Crossrefs

Cf. A111544, A111546, A111541.

Programs

PARI

{T(n,k)=local(M=matrix(n+1,n+1,m,j,if(m==j,1,if(m==j+1,-m+1, -(m-j-1)*polcoeff(log(sum(i=0,m,(i+2)!/2!*x^i)),m-j-1))))); sum(i=1,#M,(M^0-M)^i/i)[n+1,k+1]}

Formula

T(n+1, 0) = A111546(n) = A111544(n+3, 3).