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 A065432 Triangle related to Catalan triangle: recurrence related to A033877 (Schroeder numbers). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Sums of odd rows are 0, of even rows are the Catalan numbers (A000108) with alternating signs. Row sums of unsigned version give A065441. LINKS FORMULA 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}] EXAMPLE {1},{1,-1},{1,-2,0},{1,-3,1,1},{1,-4,3,2,0} CROSSREFS Sequence in context: A181940 A261209 A093555 * A094184 A078805 A122837 Adjacent sequences:  A065429 A065430 A065431 * A065433 A065434 A065435 KEYWORD sign,tabl AUTHOR Wouter Meeussen, Nov 16 2001 STATUS approved

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