A305197 Number of set partitions of [n] with symmetric block size list of length A004525(n).

1, 1, 1, 1, 3, 7, 19, 56, 171, 470, 2066, 10299, 31346, 91925, 559987, 3939653, 11954993, 36298007, 282835456, 2571177913, 7785919355, 24158837489, 229359684137, 2557117944391, 7731656573016, 24350208829581, 272633076900991, 3601150175699409, 10876116332074739

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Formula

a(n) = A275281(n,(n+sin(n*Pi/2))/2).

Maple

b:= proc(n, s) option remember; expand(`if`(n>s,
      binomial(n-1, n-s-1)*x, 1)+add(binomial(n-1, j-1)*
      b(n-j, s+j)*binomial(s+j-1, j-1), j=1..(n-s)/2)*x^2)
    end:
a:= n-> coeff(b(n, 0), x, (n+sin(n*Pi/2))/2):
seq(a(n), n=0..30);

Mathematica

b[n_, s_] := b[n, s] = Expand[If[n > s, Binomial[n - 1, n - s - 1]*x, 1] + Sum[Binomial[n - 1, j - 1]*b[n - j, s + j]*Binomial[s + j - 1, j - 1], {j, 1, (n - s)/2}]*x^2];
a[n_] := Coefficient[b[n, 0], x, (n + Sin[n*Pi/2])/2];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 13 2018, from Maple *)

Crossrefs

Bisections give A275283 (even part), A305198 (odd part).

Cf. A004525, A275281.

Sequence in context: A367484 A224031 A147586 * A071716 A306088 A188625

Adjacent sequences: A305194 A305195 A305196 * A305198 A305199 A305200

Keyword

nonn

Author

Alois P. Heinz, May 27 2018

Status

approved