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 A159965 Riordan array (1/sqrt(1-4x), (1-2x-(1-3x)c(x))/(x*sqrt(1-4x))), c(x) the g.f. of A000108. 3
 1, 2, 1, 6, 5, 1, 20, 21, 8, 1, 70, 84, 45, 11, 1, 252, 330, 220, 78, 14, 1, 924, 1287, 1001, 455, 120, 17, 1, 3432, 5005, 4368, 2380, 816, 171, 20, 1, 12870, 19448, 18564, 11628, 4845, 1330, 231, 23, 1, 48620, 75582, 77520, 54264, 26334, 8855, 2024, 300, 26, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Product of A007318 and A114422. Product of A007318^2 and A116382. Row sums are A108080. Diagonal sums are A108081. Riordan array (1/sqrt(1 - 4*x), x*c(x)^3) obtained from A092392 by taking every third column starting from column 0; x*c(x)^3 is the o.g.f. for A000245. - Peter Bala, Nov 24 2015 REFERENCES Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5. LINKS FORMULA Number triangle T(n,k) = Sum_{j = 0..n} binomial(n+k,j-k)*binomialC(n,j). T(n,k) = binomial(2*n + k, n + 2*k). - Peter Bala, Nov 24 2015 EXAMPLE Triangle begins 1, 2, 1, 6, 5, 1, 20, 21, 8, 1, 70, 84, 45, 11, 1, 252, 330, 220, 78, 14, 1, 924, 1287, 1001, 455, 120, 17, 1, 3432, 5005, 4368, 2380, 816, 171, 20, 1 PROG (MAGMA) /* As triangle */ [[Binomial(2*n+k, n+2*k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 27 2015 CROSSREFS Cf. A000245, A007318, A092392, A108080, A108081, A114422, A116382. Sequence in context: A055896 A193723 A260914 * A116395 A159924 A133367 Adjacent sequences:  A159962 A159963 A159964 * A159966 A159967 A159968 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Apr 28 2009 STATUS approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)