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Search: id:A106340
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| A106340 |
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Triangle T, read by rows, equal to the matrix inverse of the triangle defined by [T^-1](n,k) = (n-k)!*A008278(n+1,k+1), for n>=k>=0, where A008278 is a triangle of Stirling numbers of 2nd kind. |
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+0
4
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| 1, -1, 1, 1, -3, 1, -1, 9, -7, 1, 1, -45, 55, -15, 1, -1, 585, -835, 285, -31, 1, 1, -21105, 30835, -11025, 1351, -63, 1, -1, 1858185, -2719675, 977445, -121891, 6069, -127, 1, 1, -367958745, 538607755, -193649085, 24187051, -1213065, 26335, -255, 1, -1, 157169540745, -230061795355, 82717588485
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are {1,0,-1,2,-3,4,-5,6,...}. Column 1 is A106341.
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FORMULA
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T(n, k) = A106338(n, k)/k!, for n>=k>=0.
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EXAMPLE
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Triangle T begins:
1;
-1,1;
1,-3,1;
-1,9,-7,1;
1,-45,55,-15,1;
-1,585,-835,285,-31,1;
1,-21105,30835,-11025,1351,-63,1;
-1,1858185,-2719675,977445,-121891,6069,-127,1;
1,-367958745,538607755,-193649085,24187051,-1213065,26335,-255,1;
Matrix inverse begins:
1;
1,1;
2,3,1;
6,12,7,1;
24,60,50,15,1;
120,360,390,180,31,1; ...
where [T^-1](n,k) = (n-k)!*A008278(n+1,k+1).
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PROGRAM
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(PARI) {T(n, k)=(matrix(n+1, n+1, r, c, if(r>=c, (r-c)!* sum(m=0, r-c+1, (-1)^(r-c+1-m)*m^r/m!/(r-c+1-m)!)))^-1)[n+1, k+1]}
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CROSSREFS
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Cf. A106338, A008278, A106341.
Sequence in context: A145905 A144183 A050153 this_sequence A156610 A157179 A152655
Adjacent sequences: A106337 A106338 A106339 this_sequence A106341 A106342 A106343
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2005
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