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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)/2n, 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 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 June 19 15:41 EDT 2024. Contains 373503 sequences. (Running on oeis4.)