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Search: id:A089944
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| A089944 |
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Square array, read by antidiagonals, where the n-th row is the n-th binomial transform of the natural numbers, with T(0,k)=(k+1) for k>=0. |
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3
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| 1, 2, 1, 3, 3, 1, 4, 8, 4, 1, 5, 20, 15, 5, 1, 6, 48, 54, 24, 6, 1, 7, 112, 189, 112, 35, 7, 1, 8, 256, 648, 512, 200, 48, 8, 1, 9, 576, 2187, 2304, 1125, 324, 63, 9, 1, 10, 1280, 7290, 10240, 6250, 2160, 490, 80, 10, 1, 11, 2816, 24057, 45056, 34375, 14256, 3773, 704
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The main diagonal is A089945: {T(n,n)=(2*n+1)*(n+1)^(n-1), n>=0}; the hyperbinomial transform of the main diagonal is the next lower diagonal in the array (A089946): {T(n+1,n)=2*(n+1)*(n+2)^(n-1), n>=0}.
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FORMULA
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T(n, k)=(k+n+1)*(n+1)^(k-1). E.g.f.: (1+x)*exp(x)/((1-y*exp(x)).
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EXAMPLE
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Rows begin:
{1, 2, 3, 4, 5, 6, 7,..},
{1, 3, 8, 20, 48, 112, 256,..},
{1, 4, 15, 54, 189, 648, 2187,..},
{1, 5, 24, 112, 512, 2304, 10240,..},
{1, 6, 35, 200, 1125, 6250, 34375,..},
{1, 7, 48, 324, 2160, 14256, 93312,..},
{1, 8, 63, 490, 3773, 28812, 218491,..},..
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PROGRAM
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(PARI) T(n, k)=if(n<0|k<0, 0, (k+n+1)*(n+1)^(k-1))
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CROSSREFS
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Cf. A089945, A089946.
Rows : A000027, A001792, A006234, A079028, A081105, A081106, A081107, A081108, A081109, A081122. Columns : A000012, A000027, A005563
Sequence in context: A126277 A055129 A133804 this_sequence A097351 A048600 A100578
Adjacent sequences: A089941 A089942 A089943 this_sequence A089945 A089946 A089947
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 23 2003
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