A272493 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to three.

1, 4, 30, 200, 1610, 13440, 130200, 1327200, 15107400, 183321600, 2422820400, 34104470400, 515897382000, 8276556288000, 141290381232000, 2546760408192000, 48489153817104000, 970454450085120000, 20400874234060320000, 448974320483969280000

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..450

Formula

E.g.f.: x^3 * Product_{i=1..3} (i-1)!/(i!-x^i).

Recurrence: 12*a(n) = 12*n*a(n-1) + 6*(n-1)*n*a(n-2) - 4*(n-2)*(n-1)*n*a(n-3) - 2*(n-3)*(n-2)*(n-1)*n*a(n-4) - (n-4)*(n-3)*(n-2)*(n-1)*n*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*a(n-6). - Vaclav Kotesovec, May 07 2016

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(3):
seq(a(n), n=3..30);

Mathematica

FullSimplify[Table[n! * ((-35*(1 + Sqrt[2]) + 7*2^(1 + n/2)* (3*Sqrt[2] - 2) - 5*(-1)^n*(17*Sqrt[2] - 23))/2^(n/2) + 2^(5/6 - n/3)* 3^(-1 - n/3)*((11*3^(1/3) + 6*2^(1/3)* 3^(2/3))*(3 - Sqrt[2]) + 13*2^(1/6)*(3*Sqrt[2] - 2) + (26*2^(1/6)*(3*Sqrt[2] - 2) - (11*3^(1/3) + 6*2^(1/3)*3^(2/3))* (3 - Sqrt[2]))*Cos[2*n*Pi/3] + 3^(1/6)*(3 - Sqrt[2])*(11*3^(2/3) - 18*2^(1/3))*Sin[2*n*Pi/3])) / (35*(3*Sqrt[2] - 2)), {n, 3, 20}]] (* Vaclav Kotesovec, May 07 2016 *)

Crossrefs

Column k=3 of A262071.

Sequence in context: A113450 A344399 A268218 * A246151 A094567 A134093

Adjacent sequences: A272490 A272491 A272492 * A272494 A272495 A272496

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved