A365821 Total number of partitions of [n-s] whose block minima sum to s, summed over all s.

1, 0, 1, 1, 1, 2, 3, 6, 11, 23, 46, 97, 205, 448, 1004, 2339, 5661, 14291, 37507, 101962, 285386, 817772, 2386946, 7069893, 21195092, 64225525, 196636559, 608551084, 1905848637, 6049696252, 19501015441, 63960251538, 213822965681, 729536174204, 2541833303563

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Wikipedia, Partition of a set

Formula

a(7) = 6: 12|3, 134|2, 13|24, 14|23, 1|234, 123456.

a(8) = 11: 124|3, 12|34, 1345|2, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345, 1234567.

Maple

b:= proc(n, i, t, m) option remember; `if`(n=0, t^(m-i+1),
     `if`((i+m)*(m+1-i)/2<n or i>n, 0, `if`(t=0, 0,
      t*b(n, i+1, t, m))+ b(n-i, i+1, t+1, m)))
    end:
a:= n-> add(b(k, 1, 0, n-k), k=0..n):
seq(a(n), n=0..42);

Crossrefs

Antidiagonal sums of A124327.

Cf. A368102.

Sequence in context: A036590 A247139 A036591 * A036592 A036656 A001190

Adjacent sequences: A365818 A365819 A365820 * A365822 A365823 A365824

Keyword

nonn

Author

Alois P. Heinz, Dec 14 2023

Status

approved