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A272493 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to three. 2
1, 4, 30, 200, 1610, 13440, 130200, 1327200, 15107400, 183321600, 2422820400, 34104470400, 515897382000, 8276556288000, 141290381232000, 2546760408192000, 48489153817104000, 970454450085120000, 20400874234060320000, 448974320483969280000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 13:44 EST 2022. Contains 358510 sequences. (Running on oeis4.)