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A104990
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Matrix cube of triangle A104980.
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2
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1, 3, 1, 15, 6, 1, 93, 39, 9, 1, 675, 285, 75, 12, 1, 5577, 2331, 657, 123, 15, 1, 51555, 21153, 6207, 1269, 183, 18, 1, 526809, 211227, 63549, 13743, 2181, 255, 21, 1, 5895819, 2304321, 704319, 158325, 26739, 3453, 339, 24, 1, 71733585, 27291843
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OFFSET
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0,2
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COMMENTS
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Triangular matrix A104980 satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0.
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LINKS
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Table of n, a(n) for n=0..46.
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FORMULA
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T(n+1, 0) = 3*A104980(n+4, 4) for n>=0.
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EXAMPLE
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Triangle begins:
1;
3,1;
15,6,1;
93,39,9,1;
675,285,75,12,1;
5577,2331,657,123,15,1;
51555,21153,6207,1269,183,18,1;
526809,211227,63549,13743,2181,255,21,1;
5895819,2304321,704319,158325,26739,3453,339,24,1;
71733585,27291843,8424813,1947711,343641,47355,5145,435,27,1; ...
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PROG
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(PARI) {T(n, k)=if(n<k|k<0, 0, (matrix(n+1, n+1, m, j, if(m==j, 1, if(m==j+1, -m+1, -polcoeff((1-1/sum(i=0, m, i!*x^i))/x+O(x^m), m-j-1))))^-3)[n+1, k+1])}
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CROSSREFS
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Cf. A104980, A104982 (column 0), A104991 (row sums).
Sequence in context: A065250 A092589 A048966 * A089463 A136231 A113389
Adjacent sequences: A104987 A104988 A104989 * A104991 A104992 A104993
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna, Apr 10 2005
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STATUS
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approved
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