A351825 Total number of size 2 lists in all sets of lists partitioning [n] (cf. A000262).

0, 0, 2, 6, 36, 260, 2190, 21042, 226856, 2709576, 35491770, 505620830, 7780224012, 128555409996, 2269569526406, 42625044254730, 848404205856720, 17836074466842512, 394872870912995826, 9181542826326252726, 223680717959853460340, 5697036951307194432660, 151396442683371572351742

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = 2*binomial(n,2)*A000262(n-2).

E.g.f.: x^2*exp(x/(1-x)) = d/dy G(x,y)|y=1 where G(x,y) is the e.g.f. for A351823.

a(n) = Sum_{k=0..floor(n/2)} k * A351823(n,k).

a(n) ~ n^(n - 1/4) * exp(2*sqrt(n) - n - 1/2) / sqrt(2) * (1 - 101/(48*sqrt(n))). - Vaclav Kotesovec, Feb 21 2022

a(n) = 2 * A129652(n,2). - Alois P. Heinz, Feb 22 2022

Recurrence: (n-2)*a(n) = n*(2*n-5)*a(n-1) - (n-4)*(n-1)*n*a(n-2). - Vaclav Kotesovec, Mar 20 2023

Mathematica

nn = 22; Range[0, nn]! CoefficientList[Series[D[Exp[ x/(1 - x) - x ^2 + y x^2], y] /. y -> 1, {x, 0, nn}], x]
Join[{0, 0, 2}, Table[n!*Hypergeometric1F1[n-1, 2, 1]/E, {n, 3, 25}]] (* Vaclav Kotesovec, Feb 21 2022 *)

Crossrefs

Cf. A000262, A006152, A129652, A351823.

Sequence in context: A109284 A060178 A096939 * A358080 A369091 A162697

Adjacent sequences: A351822 A351823 A351824 * A351826 A351827 A351828

Keyword

nonn

Author

Geoffrey Critzer, Feb 20 2022

Status

approved