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A105629
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Triangular matrix, read by rows, equal to the matrix logarithm of triangle A105623.
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3
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also equals (1/2) the matrix logarithm of triangle A105615, since A105623 equals the matrix square-root of triangle A105615.
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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; ...
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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))}
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CROSSREFS
| Cf. A105615, A105623, A105630 (column 0), A105631 (row sums).
Sequence in context: A077907 A067346 A111541 * A085075 A058257 A083199
Adjacent sequences: A105626 A105627 A105628 * A105630 A105631 A105632
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2005
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