A110518 Riordan array (1, x*c(3x)), c(x) the g.f. of A000108.

1, 0, 1, 0, 3, 1, 0, 18, 6, 1, 0, 135, 45, 9, 1, 0, 1134, 378, 81, 12, 1, 0, 10206, 3402, 756, 126, 15, 1, 0, 96228, 32076, 7290, 1296, 180, 18, 1, 0, 938223, 312741, 72171, 13365, 2025, 243, 21, 1, 0, 9382230, 3127410, 729729, 138996, 22275, 2970, 315, 24, 1, 0

Offset

0,5

Comments

Row sums are C(3;n), A064063. Inverse is A110517. Diagonal sums are A110525.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

Number triangle: T(0,k) = 0^k, T(n,k) = (k/n)*C(2n-k-1, n-k)*3^(n-k), n > 0, k > 0.

T(n,k) = A106566(n,k)*3^(n-k). - Philippe Deléham, Nov 08 2007

Triangle T(n,k), 0 <= k <= n, read by rows, given by (0, 3, 3, 3, 3, 3, 3, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 23 2014

Example

Rows begin
  1;
  0,    1;
  0,    3,    1;
  0,   18,    6,    1;
  0,  135,   45,    9,    1;
  0, 1134,  378,   81,   12,    1;
  ...
Production matrix begins:
  0,   1;
  0,   3,   1;
  0,   9,   3,   1;
  0,  27,   9,   3,   1;
  0,  81,  27,   9,   3,   1;
  0, 243,  81,  27,   9,   3,   1;
  ... - Philippe Deléham, Sep 23 2014

Mathematica

T[0, 0] := 1; T[0, k_] := 0; T[n_, k_] := (k/n)*3^(n - k)*Binomial[2*n - k - 1, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *)

Prog

(PARI) concat([1], for(n=1, 10, for(k=0, n, print1((k/n)*3^(n-k)*binomial(2*n-k-1, n-k), ", ")))) \\ G. C. Greubel, Aug 29 2017

Crossrefs

Sequence in context: A360177 A241981 A147723 * A246049 A316773 A006837

Adjacent sequences: A110515 A110516 A110517 * A110519 A110520 A110521

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 24 2005

Status

approved