A027200 - OEIS

%I #16 May 15 2023 11:13:40

%S 0,1,0,1,0,0,3,1,0,0,3,1,0,0,0,6,2,1,0,0,0,7,2,1,0,0,0,0,12,4,2,1,0,0,

%T 0,0,14,4,2,1,0,0,0,0,0,22,6,3,2,1,0,0,0,0,0,27,7,3,2,1,0,0,0,0,0,0,

%U 40,11,5,3,2,1,0,0,0,0,0,0,49,12,5,3,2,1,0,0,0,0,0,0,0,69,17,7,4,3,2,1,0,0,0,0,0,0,0

%N Triangular array T read by rows: T(n,k) = number of partitions of n into an even number of parts, each >=k.

%F  T(n, k) = Sum{E(n, i)}, k<=i<=n, E given by A027186.

%F T(n,k) + A027199(n,k) = A026807(n,k). - _R. J. Mathar_, Oct 18 2019

%F G.f. of column k: Sum_{i>=0} x^(2*k*i)/Product_{j=1..2*i} (1-x^j). - _Seiichi Manyama_, May 15 2023

%e  Triangle begins:

%e    0;

%e    1,  0;

%e    1,  0, 0;

%e    3,  1, 0, 0;

%e    3,  1, 0, 0, 0;

%e    6,  2, 1, 0, 0, 0;

%e    7,  2, 1, 0, 0, 0, 0;

%e   12,  4, 2, 1, 0, 0, 0, 0;

%e   14,  4, 2, 1, 0, 0, 0, 0, 0;

%e   22,  6, 3, 2, 1, 0, 0, 0, 0, 0;

%e   27,  7, 3, 2, 1, 0, 0, 0, 0, 0, 0;

%e   40, 11, 5, 3, 2, 1, 0, 0, 0, 0, 0, 0;

%e   49, 12, 5, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0;

%o (PARI) T(n, k) = polcoef(sum(i=0, n, x^(2*k*i)/prod(j=1, 2*i, 1-x^j+x*O(x^n))), n); \\ _Seiichi Manyama_, May 15 2023

%Y Cf. A027186, A027187 (1st column), A027188, A027189, A027190, A027191, A027192.

%K nonn,tabl

%O 1,7

%A _Clark Kimberling_

%E More terms from _Seiichi Manyama_, May 15 2023