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 A235608 Triangle read by rows: a non-Riordan array serving as a counter-example to a conjecture about Riordan arrays. 0
 1, 2, 1, 10, 5, 1, 62, 31, 7, 1, 430, 215, 51, 10, 1, 3194, 1597, 389, 87, 12, 1, 24850, 12425, 3077, 740, 117, 15, 1, 199910, 99955, 25035, 6305, 1076, 168, 17, 1, 1649350, 824675, 208255, 54150, 9705, 1700, 208, 20, 1, 13879538, 6939769, 1763473, 469399, 87048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See Barry (2013), Example 3, for precise definition. T(n,1) = T(n,0)/2 for n>0.- Philippe Deléham, Jan 31 2014 LINKS P. Barry, Embedding structures associated with Riordan arrays and moment matrices, arXiv preprint arXiv:1312.0583, 2013. See Example 3. FORMULA G.f. for the column k (with leading zero omitted): f(x)^floor((k+2)/2))*g(x)^floor((k+1)/2)) with f(x) = (1+x-sqrt(1-10*x+x^2))/(6*x) and g(x) = (1-x-sqrt(1-10*x+x^2))/(4*x). - Philippe Deléham, Jan 31 2014 EXAMPLE Triangle begins: 1; 2, 1; 10, 5, 1; 62, 31, 7, 1; 430, 215, 51, 10, 1; 3194, 1597, 389, 87, 12, 1; 24850, 12425, 3077, 740, 117, 15, 1; 199910, 99955, 25035, 6305, 1076, 168, 17, 1; 1649350, 824675, 208255, 54150, 9705, 1700, 208, 20, 1; 13879538, 6939769, 1763473, 469399, 87048, 16449, 2248, 274, 22, 1; ... - Extended by Philippe Deléham, Jan 31 2014 MATHEMATICA f[x_] := (1+x-Sqrt[1-10*x+x^2])/(6*x); g[x_] := (1-x-Sqrt[1-10*x+x^2])/(4*x); t[n_, k_] := SeriesCoefficient[f[x]^Floor[(k+2)/2]*g[x]^Floor[(k+1)/2], {x, 0, n}]; Table[t[n-k, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 31 2014, after Philippe Deléham *) CROSSREFS The leading column is A107841. Cf. A103210, A107841, Sequence in context: A136216 A121334 A126450 * A112333 A066868 A193900 Adjacent sequences:  A235605 A235606 A235607 * A235609 A235610 A235611 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 23 2014 EXTENSIONS More terms from Philippe Deléham, Jan 31 2014 STATUS approved

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Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)