A323776 a(n) = Sum_{k = 1...n} binomial(k + 2^(n - k) - 1, k - 1).

1, 3, 7, 16, 40, 119, 450, 2253, 15207, 139190, 1731703, 29335875, 677864041, 21400069232, 924419728471, 54716596051100, 4443400439075834, 495676372493566749, 76041424515817042402, 16060385520094706930608, 4674665948889147697184915

Offset: 1

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn

Comments

Number of multiset partitions of integer partitions of 2^(n - 1) whose parts are constant and have equal sums.

Examples

			The a(1) = 1 through a(4) = 16 partitions of partitions:
  (1)  (2)     (4)           (8)
       (11)    (22)          (44)
       (1)(1)  (1111)        (2222)
               (2)(2)        (4)(4)
               (2)(11)       (4)(22)
               (11)(11)      (22)(22)
               (1)(1)(1)(1)  (4)(1111)
                             (11111111)
                             (22)(1111)
                             (1111)(1111)
                             (2)(2)(2)(2)
                             (2)(2)(2)(11)
                             (2)(2)(11)(11)
                             (2)(11)(11)(11)
                             (11)(11)(11)(11)
                             (1)(1)(1)(1)(1)(1)(1)(1)
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A000123, A001970, A002577, A006171, A007716, A034729, A047968, A279787, A279789, A305551, A306017, A319056, A323766, A323774, A323775.

Programs

Mathematica

Table[Sum[Binomial[k+2^(n-k)-1,k-1],{k,n}],{n,20}]

PARI

a(n) = sum(k=1, n, binomial(k+2^(n-k)-1, k-1)); \\ Michel Marcus, Jan 28 2019