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 A119326 Number triangle T(n,k) = Sum_{j=0..n-k} C(k,2j)*C(n-k,2j). 10
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 7, 10, 7, 1, 1, 1, 1, 11, 19, 19, 11, 1, 1, 1, 1, 16, 31, 38, 31, 16, 1, 1, 1, 1, 22, 46, 66, 66, 46, 22, 1, 1, 1, 1, 29, 64, 106, 126, 106, 64, 29, 1, 1, 1, 1, 37, 85, 162, 226, 226, 162, 85, 37, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Third column is essentially A000124. Fourth column is essentially A005448. Fifth column is A119327. Product of Pascal's triangle A007318 and A119328. Row sums are A038504. T(n,k) = T(n,n-k). REFERENCES Lukas Spiegelhofer and Jeffrey Shallit, Continuants, Run Lengths, and Barry's Modified Pascal Triangle, Volume 26(1) 2019, of The Electronic Journal of Combinatorics, #P1.31. LINKS Seiichi Manyama, Rows n = 0..139, flattened Jeffrey Shallit, Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017. FORMULA Column k has g.f.: (x^k/(1-x))* Sum{j=0..k} C(k,2j)*(x/(1-x))^(2j). T(2n,n) = A119358(n). - Alois P. Heinz, Aug 31 2018 EXAMPLE Triangle begins: 1; 1, 1; 1, 1,  1; 1, 1,  1,  1; 1, 1,  2,  1,  1; 1, 1,  4,  4,  1,  1; 1, 1,  7, 10,  7,  1, 1; 1, 1, 11, 19, 19, 11, 1, 1; CROSSREFS Cf. A119358. Sequence in context: A026584 A247342 A174547 * A219866 A333418 A212363 Adjacent sequences:  A119323 A119324 A119325 * A119327 A119328 A119329 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, May 14 2006 STATUS approved

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Last modified September 18 16:20 EDT 2021. Contains 347528 sequences. (Running on oeis4.)