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A104986
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Matrix logarithm of triangle A104980.
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4
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0, 1, 0, 2, 2, 0, 7, 4, 3, 0, 33, 14, 7, 4, 0, 191, 66, 27, 11, 5, 0, 1297, 382, 137, 48, 16, 6, 0, 10063, 2594, 843, 270, 79, 22, 7, 0, 87669, 20126, 6041, 1820, 495, 122, 29, 8, 0, 847015, 175338, 49219, 14176, 3679, 848, 179, 37, 9, 0, 8989301, 1694030, 448681
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 equals column 1 of triangular matrix A104980, which satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0. Column 1 equals twice column 0.
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FORMULA
| T(n, 0) = A104981(n), T(n+1, 1) = 2*T(n, 0) for n>=0.
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EXAMPLE
| Triangle begins:
0;
1,0;
2,2,0;
7,4,3,0;
33,14,7,4,0;
191,66,27,11,5,0;
1297,382,137,48,16,6,0;
10063,2594,843,270,79,22,7,0;
87669,20126,6041,1820,495,122,29,8,0;
847015,175338,49219,14176,3679,848,179,37,9,0;
8989301,1694030,448681,124828,31361,6930,1371,252,46,10,0; ...
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PROG
| (PARI) {T(n, k)=if(n<k|k<0, 0, sum(p=1, n+1, (-1)^p*(matrix(n+1, n+1, m, j, if(m==j, 0, if(m==j+1, -m+1, -polcoeff((1-1/sum(i=0, m, i!*x^i))/x+O(x^m), m-j-1))))^p)[n+1, k+1]/p))}
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CROSSREFS
| Cf. A104980, A104981 (column 0), A104987 (row sums).
Sequence in context: A174104 A135006 A086118 * A060007 A021457 A137456
Adjacent sequences: A104983 A104984 A104985 * A104987 A104988 A104989
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2005
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