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Search: id:A099597
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| A099597 |
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Array T(k,n) read by antidiagonals: expansion of exp(x+y)/(1-xy). |
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6
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 9, 4, 1, 1, 5, 19, 19, 5, 1, 1, 6, 33, 82, 33, 6, 1, 1, 7, 51, 229, 229, 51, 7, 1, 1, 8, 73, 496, 1313, 496, 73, 8, 1, 1, 9, 99, 919, 4581, 4581, 919, 99, 9, 1, 1, 10, 129, 1534, 11905, 32826, 11905, 1534, 129, 10, 1, 1, 11, 163, 2377
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows are polynomials in n whose coefficients are in A099599.
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FORMULA
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T(n,k) = sum {i=0..min(n,k)} C(n,i)*C(k,i)*i!^2. The LDU factorization of this square array is P * D * transpose(P), where P is Pascal's triangle A007318 and D = diag(0!^2, 1!^2, 2!^2, ... ). Compare with A088699. - Peter Bala (pbala(AT)toucansurf.com), Nov 06 2007
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EXAMPLE
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1,1,1,1,1,1,
1,2,3,4,5,6,
1,3,9,19,33,51,
1,4,19,82,229,496,
1,5,33,229,1313,4581,
1,6,51,496,4581,32826,
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CROSSREFS
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Rows include A000012, A000027, A058331. Main diagonal is A006040. Antidiagonal sums are in A099598. Cf. A099599.
Cf. A088699.
Sequence in context: A114202 A125806 A156354 this_sequence A123610 A059922 A159623
Adjacent sequences: A099594 A099595 A099596 this_sequence A099598 A099599 A099600
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Oct 28 2004
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