A027200 - OEIS

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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.

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,7

LINKS

Table of n, a(n) for n=1..105.

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:

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

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

Sequence in context: A065413 A372739 A107131 * A035654 A170846 A085604

Adjacent sequences: A027197 A027198 A027199 * A027201 A027202 A027203

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Seiichi Manyama, May 15 2023

STATUS

approved