A006200 Number of partitions into pairs. (Formerly M4263)

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

Offset

1,2

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).

Links

Table of n, a(n) for n=1..19.

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

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 *)

Crossrefs

Cf. A079267.

Sequence in context: A371776 A372210 A365840 * A243691 A151345 A281596

Adjacent sequences: A006197 A006198 A006199 * A006201 A006202 A006203

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jan 24 2017

Status

approved