A387019 Expansion of e.g.f. exp(x^4/24 * sinh(x)).

1, 0, 0, 0, 0, 5, 0, 35, 0, 126, 3150, 330, 138600, 715, 3363360, 15767115, 57657600, 2144144380, 784143360, 158880926076, 314569764600, 8351433095985, 94198076834400, 345796179437555, 15584862075108480, 28203400625412650, 1822265423987008000, 9856639365702146550

Offset

0,6

Comments

Number of ways to choose four elements from each block of the partitions of an n-set into odd blocks (see Example).

Links

Table of n, a(n) for n=0..27.

Example

a(13) = 715 since the number of ways to choose four elements from each block of the partitions of a 13-set into odd blocks are:
  Sample partition {1,2,3,4,5,6,7,8,9,10,11,12,13}: 1 partition, 715 ways.
  Note that for other partitions into odd blocks such as {1,2,3,4,5} {6,7,8,9,10} {11,12,13} it is not possible to choose four elements from each block.
a(14) = 3363360 since the number of ways are:
  Sample partition {1,2,3,4,5,6,7,8,9} {10,11,12,13,14}: 1716 such partitions, 2102100 ways.
  Sample partition {1,2,3,4,5,6,7} {8,9,10,11,12,13,14}: 2002 such partitions, 1261260 ways.

Crossrefs

Cf. A003724, A003727, A389224.

Sequence in context: A186746 A208928 A348209 * A368768 A297206 A373388

Adjacent sequences: A387016 A387017 A387018 * A387020 A387021 A387022

Keyword

nonn

Author

Enrique Navarrete, Oct 02 2025

Status

approved