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 A275326 Triangle read by rows, T(n,k) = ceiling(A275325(n,k)/2) for n>=0 and 0<=k<=n. 1
 1, 0, 1, 0, 1, 0, 3, 0, 2, 1, 0, 10, 5, 0, 5, 4, 1, 0, 35, 28, 7, 0, 14, 14, 6, 1, 0, 126, 126, 54, 9, 0, 42, 48, 27, 8, 1, 0, 462, 528, 297, 88, 11, 0, 132, 165, 110, 44, 10, 1, 0, 1716, 2145, 1430, 572, 130, 13, 0, 429, 572, 429, 208, 65, 12, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS An extension of the Catalan triangle A128899. LINKS Peter Luschny, Orbitals FORMULA T(n,k) = A275325(n,k)/2 for n>=2. T(n,1) = A057977(n) for n>=1 (the extended Catalan numbers). For odd n: T(n,1) = Sum_{k>=0} T(n+1,k). Main diagonal: T(n, floor(n/2)) = A093178(n). EXAMPLE Triangle starts: [ n] [k=0,1,2,...] [row sum] [ 0] [1] 1 [ 1] [0, 1] 1 [ 2] [0, 1] 1 [ 3] [0, 3] 3 [ 4] [0, 2, 1] 3 [ 5] [0, 10, 5] 15 [ 6] [0, 5, 4, 1] 10 [ 7] [0, 35, 28, 7] 70 [ 8] [0, 14, 14, 6, 1] 35 [ 9] [0, 126, 126, 54,  9] 315 [10] [0, 42, 48, 27, 8, 1] 126 [11] [0, 462, 528, 297, 88, 11] 1386 [12] [0, 132, 165, 110, 44, 10, 1] 462 PROG (Sage) # uses[orbital_factors] # Function orbital_factors is in A275325. def half_orbital_factors(n):     F = orbital_factors(n)     return [f//2 for f in F] if n >= 2 else F for n in (0..12): print(half_orbital_factors(n)) CROSSREFS Cf. A057977, A093178, A128899, A275324 (row sums), A275325. Sequence in context: A291786 A004603 A174951 * A092926 A052311 A181786 Adjacent sequences:  A275323 A275324 A275325 * A275327 A275328 A275329 KEYWORD nonn,tabf AUTHOR Peter Luschny, Aug 15 2016 STATUS approved

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Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)