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A027200 Triangular array T read by rows: T(n,k) = number of partitions of n into an even number of parts, each >=k.

%I A027200 #16 May 15 2023 11:13:40
%S A027200 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 A027200 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 A027200 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 A027200 Triangular array T read by rows: T(n,k) = number of partitions of n into an even number of parts, each >=k.
%F A027200  T(n, k) = Sum{E(n, i)}, k<=i<=n, E given by A027186.
%F A027200 T(n,k) + A027199(n,k) = A026807(n,k). - _R. J. Mathar_, Oct 18 2019
%F A027200 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 A027200  Triangle begins:
%e A027200    0;
%e A027200    1,  0;
%e A027200    1,  0, 0;
%e A027200    3,  1, 0, 0;
%e A027200    3,  1, 0, 0, 0;
%e A027200    6,  2, 1, 0, 0, 0;
%e A027200    7,  2, 1, 0, 0, 0, 0;
%e A027200   12,  4, 2, 1, 0, 0, 0, 0;
%e A027200   14,  4, 2, 1, 0, 0, 0, 0, 0;
%e A027200   22,  6, 3, 2, 1, 0, 0, 0, 0, 0;
%e A027200   27,  7, 3, 2, 1, 0, 0, 0, 0, 0, 0;
%e A027200   40, 11, 5, 3, 2, 1, 0, 0, 0, 0, 0, 0;
%e A027200   49, 12, 5, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0;
%o A027200 (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 A027200 Cf. A027186, A027187 (1st column), A027188, A027189, A027190, A027191, A027192.
%K A027200 nonn,tabl
%O A027200 1,7
%A A027200 _Clark Kimberling_
%E A027200 More terms from _Seiichi Manyama_, May 15 2023