A111542 -id:A111542

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A111541

Matrix logarithm of triangle A111536.

+10
6

0, 1, 0, 3, 2, 0, 14, 5, 3, 0, 84, 22, 8, 4, 0, 600, 128, 36, 12, 5, 0, 4908, 896, 212, 58, 17, 6, 0, 44952, 7220, 1496, 360, 90, 23, 7, 0, 454344, 65336, 12128, 2652, 602, 134, 30, 8, 0, 5016768, 653720, 110288, 22320, 4736, 974, 192, 38, 9, 0, 60062352, 7155104

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Column 0 (A111538) is found in column 2 of triangle A111536.

LINKS

Table of n, a(n) for n=0..56.

EXAMPLE

Triangle begins:

1,0;

3,2,0;

14,5,3,0;

84,22,8,4,0;

600,128,36,12,5,0;

4908,896,212,58,17,6,0;

44952,7220,1496,360,90,23,7,0;

454344,65336,12128,2652,602,134,30,8,0;

5016768,653720,110288,22320,4736,974,192,38,9,0; ...

PROG

(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+1)!/1!*x^i)), m-j-1))))); return(if(n<k || k<0, 0, sum(i=1, #M, (M^0-M)^i/i)[n+1, k+1]))

CROSSREFS

Cf. A111536, A111538 (column 0), A111542 (column 1), A111543 (column 2).

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Aug 06 2005

STATUS

approved

A111543

Column 2 of triangle A111541, which is the matrix logarithm of A111536.

+10
2

0, 3, 8, 36, 212, 1496, 12128, 110288, 1108064, 12171872, 145061120, 1864321472, 25710635648, 378871778432, 5943632568320, 98936446059776, 1742232571097600, 32367994818881024, 632845309575139328, 12991224275641441280

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

PROG

(PARI) {a(n)=local(M=matrix(n+3, n+3, m, j, if(m==j, 1, if(m==j+1, -m+1, -(m-j-1)*polcoeff(log(sum(i=0, m, (i+1)!/1!*x^i)), m-j-1))))); if(n<0, 0, sum(i=1, #M, (M^0-M)^i/i)[n+3, 3])}