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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.
1
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, 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, 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
OFFSET
1,7
FORMULA
T(n, k) = Sum{E(n, i)}, k<=i<=n, E given by A027186.
T(n,k) + A027199(n,k) = A026807(n,k). - R. J. Mathar, Oct 18 2019
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
EXAMPLE
Triangle begins:
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, 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;
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;
PROG
(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
CROSSREFS
Sequence in context: A065413 A372739 A107131 * A035654 A170846 A085604
KEYWORD
nonn,tabl
EXTENSIONS
More terms from Seiichi Manyama, May 15 2023
STATUS
approved