cp's OEIS Frontend

A034929 A triangle of Motzkin ballot numbers, read by rows.

%I A034929 #8 Jul 08 2025 21:28:29
%S A034929 1,1,1,1,2,1,1,3,3,2,1,4,6,6,4,1,5,10,13,13,9,1,6,15,24,30,30,21,1,7,
%T A034929 21,40,59,72,72,51,1,8,28,62,105,148,178,178,127,1,9,36,91,174,276,
%U A034929 378,450,450,323,1,10,45,128,273,480,730,980,1158,1158,835,1,11,55,174,410,791
%N A034929 A triangle of Motzkin ballot numbers, read by rows.
%C A034929 Mirror image of A091836. Row sums are the Motzkin numbers (A001006). T(n,n-1)=A001006(n-2) (the Motzkin numbers). T(n,n-2)=A005554(n-1).
%D A034929 M. Aigner, Motzkin numbers, Europ. J. Comb. 19 (1998), 663-675.
%F A034929 G.f.= 2(1+tz)/[1-2z+tz-2tz^2+sqrt(1-2tz-3t^2*z^2)].
%e A034929 Triangle begins:
%e A034929 [1],
%e A034929 [1, 1],
%e A034929 [1, 2, 1],
%e A034929 [1, 3, 3, 2],
%e A034929 [1, 4, 6, 6, 4],
%e A034929 [1, 5, 10, 13, 13, 9],
%e A034929 [1, 6, 15, 24, 30, 30, 21],
%e A034929 [1, 7, 21, 40, 59, 72, 72, 51]
%Y A034929 Cf. A001006, A091836, A005554.
%K A034929 nonn,tabl
%O A034929 1,5
%A A034929 _N. J. A. Sloane_
%E A034929 Edited by _Emeric Deutsch_, Mar 11 2004