A105629 Triangular matrix, read by rows, equal to the matrix logarithm of triangle A105623.

0, 1, 0, 3, 2, 0, 17, 7, 3, 0, 135, 43, 13, 4, 0, 1353, 361, 93, 21, 5, 0, 16251, 3779, 883, 175, 31, 6, 0, 226857, 47077, 10277, 1893, 297, 43, 7, 0, 3605775, 678443, 140743, 24735, 3631, 467, 57, 8, 0, 64288209, 11095201, 2211413, 376209, 52961, 6385, 693

Offset

0,4

Comments

Also equals (1/2) the matrix logarithm of triangle A105615, since A105623 equals the matrix square-root of triangle A105615.

Links

Table of n, a(n) for n=0..51.

Example

Triangle begins:
0;
1,0;
3,2,0;
17,7,3,0;
135,43,13,4,0;
1353,361,93,21,5,0;
16251,3779,883,175,31,6,0;
226857,47077,10277,1893,297,43,7,0;
3605775,678443,140743,24735,3631,467,57,8,0;
64288209,11095201,2211413,376209,52961,6385,693,73,9,0; ...

Prog

(PARI) T(n, k)=local(L, M=matrix(n+1, n+1, m, j, if(m>=j, if(m==j, 1, if(m==j+1, -2*j, polcoeff(1/sum(i=0, m-j, (2*i)!/i!/2^i*x^i)+O(x^m), m-j)))))^-1); L=sum(i=1, #M, (-1)^(i-1)*(M-M^0)^i/i); return(if(n<k || k<0, 0, L[n+1, k+1]/2))

Crossrefs

Cf. A105615, A105623, A105630 (column 0), A105631 (row sums).

Sequence in context: A111541 A371025 A244134 * A085075 A321518 A267883

Adjacent sequences: A105626 A105627 A105628 * A105630 A105631 A105632

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 16 2005

Status

approved