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A272515 Number of set partitions of [n] into three blocks with distinct sizes. 2
60, 105, 448, 2016, 4980, 15675, 61644, 155155, 482573, 1733550, 4549808, 13890360, 48104628, 128949675, 392009140, 1322692581, 3607864403, 10929721440, 36245555284, 100109572875, 302709337515, 990788537700, 2763564406113, 8344789976616, 27039048750600 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..1000

FORMULA

a(n) = n! * [x^n*y^3] Product_{n>=1} (1+y*x^n/n!).

Conjecture: a(n) ~ 3^n / 6. - Vaclav Kotesovec, Dec 11 2020

MAPLE

b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n

      or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n, i))))

    end:

a:= n-> b(n$2, 3):

seq(a(n), n=6..40);

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[t > i || t(t+1)/2 > n || t(2i+1-t)/2 < n, 0, If[n == 0, 1, b[n, i - 1, t] + If[i > n, 0, b[n - i, i - 1, t - 1]* Binomial[n, i]]]];

a[n_] := b[n, n, 3];

a /@ Range[6, 40] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A131632.

Sequence in context: A267434 A048934 A097714 * A043221 A039398 A044001

Adjacent sequences:  A272512 A272513 A272514 * A272516 A272517 A272518

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified November 28 13:04 EST 2021. Contains 349408 sequences. (Running on oeis4.)