A006200 Number of partitions into pairs.

1, 6, 55, 610, 7980, 120274, 2052309, 39110490, 823324755, 18974858540, 475182478056, 12848667150956, 373081590628565, 11578264139795430, 382452947343624515, 13397354334102974934, 496082324933446766724, 19360538560004548357830, 794275868644522931369185

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A079267.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
     (n*(4*n^2-7)*a(n-1)+(n+1)*(2*n+1)*a(n-2))/((2*n-1)*(n-1)))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 24 2017

Mathematica

Table[(2*n+1)! * Hypergeometric1F1[1-n, -1-2*n, -2] / (3*2^n*(n-1)!), {n, 1, 20}] (* Vaclav Kotesovec, Jan 24 2017 *)

Formula

a(n) = A079267(n + 2, 3). - Sean A. Irvine, Jan 24 2017

a(n) ~ 2^(n + 3/2) * n^(n + 2) / (3 * exp(n + 1)). - Vaclav Kotesovec, May 20 2018

Extensions

More terms from Sean A. Irvine, Jan 24 2017