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A167630 Riordan array (1/(1-x),xm(x)) where m(x) is the g.f. of Motzkin numbers A001006. 2
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 8, 4, 1, 1, 17, 20, 13, 5, 1, 1, 38, 50, 38, 19, 6, 1, 1, 89, 126, 107, 63, 26, 7, 1, 1, 216, 322, 296, 196, 96, 34, 8, 1, 1, 539, 834, 814, 588, 326, 138, 43, 9, 1, 1, 1374, 2187, 2236, 1728, 1052, 507, 190, 53, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Diagonal sums : A082395.

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

FORMULA

T(n,0)=1, T(0,k)=0 for k>0, T(n,k)=0 if k>n, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-1,k+1).

Sum_{k=0..n} k * T(n,k) = A003462(n). - Alois P. Heinz, Apr 20 2018

EXAMPLE

Triangle begins:

1;

1,  1;

1,  2,  1;

1,  4,  3,  1;

1,  8,  8,  4,  1;

1, 17, 20, 13,  5, 1;

1, 38, 50, 38, 19, 6, 1;

...

MAPLE

T:= proc(n, k) option remember; `if`(k=0, 1,

      `if`(k>n, 0, T(n-1, k-1)+T(n-1, k)+T(n-1, k+1)))

    end:

seq(seq(T(n, k), k=0..n), n=0..12);  # Alois P. Heinz, Apr 20 2018

CROSSREFS

Diagonals include: A006416, A034856, A086615, A140662.

Cf. A001006, A003462, A064189, A094531.

Sequence in context: A055587 A137743 A099239 * A322264 A009998 A113993

Adjacent sequences:  A167627 A167628 A167629 * A167631 A167632 A167633

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Nov 07 2009

STATUS

approved

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Last modified October 23 09:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)