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A238589
Number of partitions p of n such that 2*min(p) is a part of p.
6
0, 0, 1, 1, 2, 4, 5, 8, 13, 17, 24, 36, 47, 64, 88, 116, 153, 203, 261, 340, 439, 559, 710, 905, 1136, 1427, 1786, 2223, 2756, 3415, 4201, 5167, 6330, 7730, 9413, 11449, 13864, 16767, 20225, 24344, 29228, 35045, 41898, 50029, 59609, 70899, 84165, 99785, 118052
OFFSET
1,5
LINKS
FORMULA
a(n) = A000041(n) - A238594(n).
G.f.: Sum_{k>=1} x^(3*k)/Product_{j>=k} (1-x^j). - Seiichi Manyama, May 17 2023
EXAMPLE
a(6) counts these partitions: 42, 321, 2211, 21111.
MATHEMATICA
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 50}]
PROG
(PARI) my(N=50, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/prod(j=k, N, 1-x^j)))) \\ Seiichi Manyama, May 17 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2014
STATUS
approved