A387809 Expansion of e.g.f. exp(cosh(x)*x^2/2).

1, 1, 9, 120, 3073, 106200, 5127771, 314285062, 24078410385, 2228867998488, 244849662313795, 31371399215727186, 4625612331118866825, 776006776909391907100, 146700411086352937966803, 30993780039470456902274190, 7265544892972254169186749601, 1877900179127585790240867476112

Offset

0,3

Comments

Number of ways to choose two elements from each block of the partitions of a 2n-set into even blocks (see example).

Links

Table of n, a(n) for n=0..17.

Example

Seen as even groups of a total of 2*n people, the number of ways to choose two people from each group (block) for n=4 is (number of people in parentheses):
  1 group (8): 28 ways;
  2 groups (6,2): 420 ways;
  2 groups (4,4): 1260 ways;
  3 groups (4,2,2): 1260 ways;
  4 groups (2,2,2,2): 105 ways, for a total of 3073 ways.

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-2*j)*
      binomial(n-1, 2*j-1)*binomial(2*j, 2), j=1..n/2))
    end:
a:= n-> b(2*n):
seq(a(n), n=0..17);  # Alois P. Heinz, Sep 08 2025

Crossrefs

Cf. A005046, A009233.

Sequence in context: A384828 A024487 A002691 * A379123 A234320 A157930

Adjacent sequences: A387806 A387807 A387808 * A387810 A387811 A387812

Keyword

nonn

Author

Enrique Navarrete, Sep 08 2025

Status

approved