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 A271763 Number of set partitions of [n] with minimal block length multiplicity equal to three. 2
 1, 0, 0, 15, 0, 0, 1540, 3150, 24255, 81235, 496210, 605605, 36987951, 13833820, 849333940, 24419945732, 111237098546, 1219799147204, 16146398449224, 109697049177254, 1037441240056529, 9042707959752775, 84237798887033660, 614681985047225810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..576 Wikipedia, Partition of a set FORMULA a(n) = A271424(n,3). EXAMPLE a(6) = 15: 12|34|56, 12|35|46, 12|36|45, 13|24|56, 13|25|46, 13|26|45, 14|23|56, 15|23|46, 16|23|45, 14|25|36, 14|26|35, 15|24|36, 16|24|35, 15|26|34, 16|25|34. MAPLE with(combinat): b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(multinomial(n, n-i*j, i\$j) *b(n-i*j, i-1, k)/j!, j={0, \$k..n/i}))) end: a:= n-> b(n\$2, 3)-b(n\$2, 4): seq(a(n), n=3..30); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]]}]]]; a[n_] := b[n, n, 3] - b[n, n, 4]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *) CROSSREFS Column k=3 of A271424. Sequence in context: A324677 A324675 A106239 * A362267 A271339 A202857 Adjacent sequences: A271760 A271761 A271762 * A271764 A271765 A271766 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 13 2016 STATUS approved

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Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)