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A272517 Number of set partitions of [n] into five blocks with distinct sizes. 2
37837800, 100900800, 588107520, 2977294320, 20020160160, 164118754800, 635661248040, 3295178686800, 17741374681800, 95826446465904, 623399389674600, 2664090278249400, 13876038856379700, 71797074694745400, 375274098870636420, 2199911433079733100 (list; graph; refs; listen; history; text; internal format)
OFFSET

15,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 15..1000

FORMULA

a(n) = n! * [x^n*y^5] Product_{n>=1} (1+y*x^n/n!).

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, 5):

seq(a(n), n=15..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, 5];

a /@ Range[15, 40] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A131632.

Sequence in context: A034645 A204054 A206196 * A246232 A248710 A342350

Adjacent sequences:  A272514 A272515 A272516 * A272518 A272519 A272520

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified January 16 13:35 EST 2022. Contains 350376 sequences. (Running on oeis4.)