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Search: id:A102051
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| A102051 |
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Matrix inverse of triangle A101275 (number of Schroeder paths). |
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+0
3
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| 1, -1, 1, 3, -4, 1, -9, 15, -7, 1, 31, -58, 36, -10, 1, -113, 229, -170, 66, -13, 1, 431, -924, 775, -372, 105, -16, 1, -1697, 3795, -3481, 1939, -691, 153, -19, 1, 6847, -15822, 15542, -9674, 4072, -1154, 210, -22, 1, -28161, 66801, -69276, 47012, -22446, 7606, -1788, 276, -25, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are {1,0,0,0...}. Absolute row sums form A006139. Column 0 forms signed A052709. Column 1 forms A102052. Column 2 forms A102053.
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FORMULA
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G.f.: 2/(1+y+(1-y)*sqrt(1+4*x-4*x^2)).
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EXAMPLE
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Rows begin:
[1],
[ -1,1],
[3,-4,1],
[ -9,15,-7,1],
[31,-58,36,-10,1],
[ -113,229,-170,66,-13,1],
[431,-924,775,-372,105,-16,1],
[ -1697,3795,-3481,1939,-691,153,-19,1],
[6847,-15822,15542,-9674,4072,-1154,210,-22,1],...
Matrix inverse equals triangle A101275:
[1],
[1,1],
[1,4,1],
[1,13,7,1],
[1,44,34,10,1],...
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PROGRAM
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(PARI) {T(n, k)=polcoeff(polcoeff(2/(2*y+(1-y)*(1+sqrt(1+4*x-4*x^2+x*O(x^n)))), n)+y*O(y^k), k)}
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CROSSREFS
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Cf. A101275, A006139, A052709, A102052, A102053.
Sequence in context: A105578 A010611 A136158 this_sequence A078068 A054649 A138263
Adjacent sequences: A102048 A102049 A102050 this_sequence A102052 A102053 A102054
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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), Dec 27 2004
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