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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 MATHEMATICA T[_, 0] = T[n_, n_] = 1; T[n_, k_] /; 0

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Last modified August 9 20:04 EDT 2024. Contains 375044 sequences. (Running on oeis4.)