A271768 Number of set partitions of [n] with minimal block length multiplicity equal to eight.
1, 0, 0, 0, 0, 0, 0, 0, 2027025, 0, 0, 0, 0, 0, 0, 0, 10652498631775, 4141161399375, 64602117830250, 26428139112375, 2096632369581750, 137561852302875, 80768458994973750, 609202488769875, 158980016052580597875, 353341814230502847750, 1344898884799733513250
Offset: 8
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 8..578
- Wikipedia, Partition of a set
Crossrefs
Column k=8 of A271424.
Programs
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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, 8)-b(n$2, 9): seq(a(n), n=8..35);
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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, 8] - b[n, n, 9]; Table[a[n], {n, 8, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
Formula
a(n) = A271424(n,8).