A274762 Number of sequences with up to n copies each of 1,2,...,n.

1, 2, 19, 5248, 191448941, 1856296498826906, 7843008902239185171370147, 21408941228439913825832318523364743824, 52400635808473472283994952631626957015306076632624953, 152306240915343870544748050434914720360496623911547121447677238156864610

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..26

Formula

a(n) ~ exp(11/12) * n^(n^2 - n/2 + 1) / (2*Pi)^((n-1)/2). - Vaclav Kotesovec, May 24 2020

Example

a(0) = 1: () = the empty sequence.
a(1) = 2: (), 1.
a(2) = 19: (), 1, 2, 11, 12, 21, 22, 112, 121, 122, 211, 212, 221, 1122, 1212, 1221, 2112, 2121, 2211.

Maple

b:= proc(n, k, i) option remember; `if`(k=0, 1,
     `if`(i<1, 0, add(b(n, k-j, i-1)/j!, j=0..min(k, n))))
    end:
a:= n-> add(b(n, k, n)*k!, k=0..n^2):
seq(a(n), n=0..10);

Mathematica

Table[Sum[k!*SeriesCoefficient[Sum[x^j/j!, {j, 0, n}]^n, {x, 0, k}], {k, 0, n^2}], {n, 0, 10}] (* Vaclav Kotesovec, May 24 2020 *)

Prog

(PARI) {a(n) = sum(i=0, n^2, i!*polcoef(sum(j=0, n, x^j/j!)^n, i))} \\ Seiichi Manyama, May 19 2019

Crossrefs

Row sums of A234574.

Main diagonal of A308292.

Cf. A000312, A034841.

Sequence in context: A365050 A024229 A094663 * A091688 A306207 A355466

Adjacent sequences: A274759 A274760 A274761 * A274763 A274764 A274765

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2016

Status

approved