A119335 - OEIS

%I #16 Sep 14 2023 03:40:24

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,5,5,1,

%T 1,1,1,1,1,11,17,11,1,1,1,1,1,1,21,41,41,21,1,1,1,1,1,1,36,81,101,81,

%U 36,1,1,1,1,1,1,57,141,201,201,141,57,1,1,1

%N Number triangle T(n,k) = Sum_{j=0..n-k} C(k,3j)*C(n-k,3j).

%C Row sums are A119336. Product of Pascal's triangle and A119337.

%H Seiichi Manyama, <a href="/A119335/b119335.txt">Rows n = 0..139, flattened</a>

%F Column k has g.f. (x^k/(1-x)) * Sum_{j=0..k} C(k,3j)(x/(1-x))^(3j).

%e Triangle begins

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 1,  1;

%e 1, 1, 1,  1,  1;

%e 1, 1, 1,  1,  1,   1;

%e 1, 1, 1,  2,  1,   1,  1;

%e 1, 1, 1,  5,  5,   1,  1,  1;

%e 1, 1, 1, 11, 17,  11,  1,  1, 1;

%e 1, 1, 1, 21, 41,  41, 21,  1, 1, 1;

%e 1, 1, 1, 36, 81, 101, 81, 36, 1, 1, 1;

%t T[n_, k_] := Sum[Binomial[k, 3j] Binomial[n-k, 3j], {j, 0, n-k}];

%t Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Sep 14 2023 *)

%Y T(2n,n) gives A119363.

%Y Cf. A119326.

%K easy,nonn,tabl

%O 0,25

%A _Paul Barry_, May 14 2006

%E More terms from _Seiichi Manyama_, Mar 12 2019