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A089962
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Triangle, read by rows, that equals the matrix inverse of A071207 when treated as a lower triangular matrix.
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1
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1, -1, 1, 0, -4, 1, 0, 9, -9, 1, 0, -16, 48, -16, 1, 0, 25, -200, 150, -25, 1, 0, -36, 720, -1080, 360, -36, 1, 0, 49, -2352, 6615, -3920, 735, -49, 1, 0, -64, 7168, -36288, 35840, -11200, 1344, -64, 1, 0, 81, -20736, 183708, -290304, 141750, -27216, 2268, -81, 1, 0, -100, 57600, -874800, 2150400, -1575000, 453600
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| A071207 describes the transform of a sequence B that results in a sequence D defined by: "d(n) = the (n+1)-th term of the n-th binomial transform of sequence B". Then d(n)=sum(k=0..n, A071207(n,k)*b(k)) for n>=0, where A071207(n,k)=n^(n-k)*C(n,k). The matrix inverse of A071207 describes the inverse transform that yields B from D: b(n)=sum(k=0..n,T(n,k)*d(k)) for n>=0, where T(0,0)=1, T(n,k)=(-1)^(n-k)*C(n,k)*n*k^(n-k-1) for 0<k<=n.
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FORMULA
| T(n, k)=(-1)^(n-k)*C(n, k)*n*k^(n-k-1) for 0<k<=n, with T(0, 0)=1. O.g.f.: A(x, y)=(1-y)*sum_{n>=0}x^n*y^n/(1+n*y)^(n+2).
E.g.f. (1-y)*exp(x*y*exp(-y)) - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 18 2003
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EXAMPLE
| Rows begin:
{1},
{-1,1},
{0,-4,1},
{0,9,-9,1},
{0,-16,48,-16,1},
{0,25,-200,150,-25,1},
{0,-36,720,-1080,360,-36,1},
{0,49,-2352,6615,-3920,735,-49,1},
{0,-64,7168,-36288,35840,-11200,1344,-64,1},
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PROG
| (PARI) T(n, k)=if(k<0|k>n, 0, if(n==0&k==0, 1, (-1)^(n-k)*binomial(n, k)*n*k^(n-k-1)))
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CROSSREFS
| Cf. A071207.
Sequence in context: A050465 A134575 A095831 * A127155 A145880 A048516
Adjacent sequences: A089959 A089960 A089961 * A089963 A089964 A089965
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KEYWORD
| sign,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 17 2003
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