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A104988
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Matrix square of triangle A104980.
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4
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1, 2, 1, 8, 4, 1, 42, 20, 6, 1, 266, 120, 38, 8, 1, 1954, 836, 270, 62, 10, 1, 16270, 6616, 2150, 516, 92, 12, 1, 151218, 58576, 19030, 4688, 882, 128, 14, 1, 1551334, 573672, 185674, 46516, 9050, 1392, 170, 16, 1, 17414114, 6159976, 1982310, 502324, 99994
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Triangular matrix A104980 satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0.
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FORMULA
| T(n+1, 0) = 2*A104980(n+3, 3) = 2*A104982(n) for n>=0.
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EXAMPLE
| Triangle begins:
1;
2,1;
8,4,1;
42,20,6,1;
266,120,38,8,1;
1954,836,270,62,10,1;
16270,6616,2150,516,92,12,1;
151218,58576,19030,4688,882,128,14,1;
1551334,573672,185674,46516,9050,1392,170,16,1;
17414114,6159976,1982310,502324,99994,15956,2070,218,18,1; ...
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PROG
| (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))))^-2)[n+1, k+1])}
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CROSSREFS
| Cf. A104980, A104982 (column 0), A104989 (row sums).
Sequence in context: A110446 A109979 A110171 * A136225 A089460 A178102
Adjacent sequences: A104985 A104986 A104987 * A104989 A104990 A104991
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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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