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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
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-François Alcover, Dec 11 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A131632.
Sequence in context: A034645 A204054 A206196 * A246232 A248710 A342350
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2016
STATUS
approved

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Last modified June 19 15:41 EDT 2024. Contains 373503 sequences. (Running on oeis4.)