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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)/2n, 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-François 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.)