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Search: id:A137156
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| A137156 |
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Matrix inverse of triangle A137153(n,k) = C(2^k+n-k-1, n-k), read by rows. |
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+0
7
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| 1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 9, -24, 22, -8, 1, -88, 239, -228, 92, -16, 1, 1802, -4920, 4749, -1976, 376, -32, 1, -75598, 206727, -200240, 84086, -16432, 1520, -64, 1, 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Unsigned column 0 = A001192, number of full sets of size n.
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FORMULA
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G.f. of column k: 1 = Sum_{n>=0} T(n+k,k)*x^n/(1-x)^(2^(n+k)).
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EXAMPLE
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Triangle begins:
1;
-1, 1;
1, -2, 1;
-2, 5, -4, 1;
9, -24, 22, -8, 1;
-88, 239, -228, 92, -16, 1;
1802, -4920, 4749, -1976, 376, -32, 1;
-75598, 206727, -200240, 84086, -16432, 1520, -64, 1;
6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1; ...
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PROGRAM
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(PARI) /* As matrix inverse of A137153: */ {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(2^(c-1)+r-c-1, r-c)))); if(n<k|k<0, 0, (M^-1)[n+1, k+1]} (PARI) /* Using the g.f.: */ {T(n, k)=if(n<k|k<0, 0, if(n==k, 1, polcoeff(1-sum(j=0, n-k-1, T(j+k, k)*x^j/(1-x+x*O(x^(n-k)))^(2^(j+k))), n-k)))}
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CROSSREFS
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Cf. A137153 (matrix inverse); unsigned columns: A001192, A137157, A137158, A137159; unsigned row sums: A137160.
Adjacent sequences: A137153 A137154 A137155 this_sequence A137157 A137158 A137159
Sequence in context: A099602 A104560 A121435 this_sequence A136457 A078016 A078046
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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), Jan 24 2008
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