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 A099557 Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x). 2
 1, 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 4, 3, 1, 0, 1, 5, 6, 4, 0, 0, 1, 6, 10, 10, 1, 0, 0, 1, 7, 15, 20, 5, 1, 0, 0, 1, 8, 21, 35, 15, 6, 0, 0, 0, 1, 9, 28, 56, 35, 21, 1, 0, 0, 0, 1, 10, 36, 84, 70, 56, 7, 1, 0, 0, 0, 1, 11, 45, 120, 126, 126, 28, 8, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums form A005314. Antidiagonal sums form A099558. LINKS FORMULA G.f.: (1-x+x*y)/((1-x)^2-x^3*y^2). EXAMPLE Rows begin: [1], [1,1], [1,2,0], [1,3,1,0], [1,4,3,1,0], [1,5,6,4,0,0], [1,6,10,10,1,0,0], [1,7,15,20,5,1,0,0], [1,8,21,35,15,6,0,0,0], [1,9,28,56,35,21,1,0,0,0], [1,10,36,84,70,56,7,1,0,0,0],... and can be derived from Pascal's triangle by shifting each column k down by [k/2] rows. PROG (PARI) {T(n, k)=polcoeff(polcoeff((1-x+x*y)/((1-x)^2-x^3*y^2)+x*O(x^n), n, x)+y*O(y^k), k, y)} CROSSREFS Cf. A005314, A099558. Sequence in context: A174067 A124943 A169803 * A214576 A079217 A079221 Adjacent sequences:  A099554 A099555 A099556 * A099558 A099559 A099560 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Oct 22 2004 STATUS approved

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Last modified April 8 12:16 EDT 2020. Contains 333314 sequences. (Running on oeis4.)