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A027199
Triangular array T read by rows: T(n,k) = number of partitions of n into an odd number of parts, each >=k.
1
1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 8, 2, 1, 1, 1, 1, 1, 10, 3, 1, 1, 1, 1, 1, 1, 16, 4, 2, 1, 1, 1, 1, 1, 1, 20, 6, 2, 1, 1, 1, 1, 1, 1, 1, 29, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 37, 10, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 52, 12, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 66, 17, 6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,4
FORMULA
T(n, k) = Sum{O(n, i)}, k<=i<=n, O given by A027185.
T(n,k) + A027200(n,k) = A026807(n,k). - R. J. Mathar, Oct 18 2019
G.f. of column k: x^k * Sum_{i>=0} x^(2*k*i)/Product_{j=1..2*i+1} (1-x^j). - Seiichi Manyama, May 15 2023
EXAMPLE
Triangle begins:
1;
1, 1;
2, 1, 1;
2, 1, 1, 1;
4, 1, 1, 1, 1;
5, 2, 1, 1, 1, 1;
8, 2, 1, 1, 1, 1, 1;
10, 3, 1, 1, 1, 1, 1, 1;
16, 4, 2, 1, 1, 1, 1, 1, 1;
20, 6, 2, 1, 1, 1, 1, 1, 1, 1;
29, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1;
37, 10, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1;
52, 12, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1;
PROG
(PARI) T(n, k) = polcoef(x^k*sum(i=0, n, x^(2*k*i)/prod(j=1, 2*i+1, 1-x^j+x*O(x^n))), n); \\ Seiichi Manyama, May 15 2023
CROSSREFS
Sequence in context: A026835 A117975 A143258 * A140218 A193805 A159704
KEYWORD
nonn,tabl
EXTENSIONS
More terms from Seiichi Manyama, May 15 2023
STATUS
approved