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 A285918 Number of ordered set partitions of [n] into three blocks such that equal-sized blocks are ordered with increasing least elements. 3
 1, 18, 75, 420, 1218, 4242, 14563, 42930, 132528, 432960, 1250340, 3814629, 12073701, 35074482, 106044555, 331913202, 967193328, 2917846758, 9062084298, 26507831559, 79848170823, 246771097680, 723922691700, 2178960263415, 6709005218503, 19728686792637 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..1000 Wikipedia, Partition of a set MAPLE b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat       [multinomial](n, n-i*j, i\$j)/j!^2, j=0..n/i)), x, 4)     end: a:= n-> coeff(b(n\$2, 0), x, 3): seq(a(n), n=3..30); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i-1, p+j]*multinomial[n, Join[{n - i*j}, Table[i, j] ] ]/j!^2, {j, 0, n/i}]], {x, 0, 4}]; a[n_] := Coefficient[b[n, n, 0], x, 3]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *) CROSSREFS Column k=3 of A285824. Cf. A285854. Sequence in context: A284659 A143666 A139757 * A262402 A296363 A164603 Adjacent sequences:  A285915 A285916 A285917 * A285919 A285920 A285921 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 28 2017 STATUS approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)