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Search: id:A065432
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| A065432 |
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Triangle related to Catalan triangle: recurrence related to A033877 (Schroeder numbers). |
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+0
3
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| 1, 1, -1, 1, -2, 0, 1, -3, 1, 1, 1, -4, 3, 2, 0, 1, -5, 6, 2, -2, -2, 1, -6, 10, 0, -6, -4, 0, 1, -7, 15, -5, -11, -3, 5, 5, 1, -8, 21, -14, -15, 4, 15, 10, 0, 1, -9, 28, -28, -15, 19, 26, 6, -14, -14, 1, -10, 36, -48, -7, 42, 30, -16, -42, -28, 0, 1, -11, 45, -75, 14, 70, 16, -60, -70, -14, 42, 42, 1, -12, 55, -110, 54, 96, -28, -120
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OFFSET
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0,5
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COMMENT
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Sums of odd rows are 0, of even rows are the Catalan numbers (A000108) with alternating signs. Row sums of unsigned version give A065441.
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FORMULA
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a[0, 0] := 1; a[n_, k_] := 0/;(k > n||n < 0||k < 0); a[n_, k_] := a[n, k] = a[n, k-1]-2a[n-1, k-1]+a[n-1, k]; Table[a[n, k], {n, 0, 16}, {k, 0, n}]
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EXAMPLE
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{1},{1,-1},{1,-2,0},{1,-3,1,1},{1,-4,3,2,0}
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CROSSREFS
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Sequence in context: A026794 A137712 A093555 this_sequence A094184 A078805 A122837
Adjacent sequences: A065429 A065430 A065431 this_sequence A065433 A065434 A065435
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KEYWORD
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sign
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 16 2001
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