A159965 Riordan array (1/sqrt(1-4x), (1-2x-(1-3x)c(x))/(x*sqrt(1-4x))), c(x) the g.f. of A000108.

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

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

Links

Table of n, a(n) for n=0..54.

Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.

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