A305198 Number of set partitions of [2n+1] with symmetric block size list of length A109613(n).

1, 1, 7, 56, 470, 10299, 91925, 3939653, 36298007, 2571177913, 24158837489, 2557117944391, 24350208829581, 3601150175699409, 34626777577615921, 6820331445080882282, 66066554102006208712, 16719951521837764142510, 162903256982698962545956

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = A275281(2n+1,A109613(n)).

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(2*n+1, 0), x, n+irem(n+1, 2)):
seq(a(n), n=0..20);

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[2n + 1, 0], x, n + Mod[n + 1, 2]];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

Crossrefs

Bisection (odd part) of A305197.

Cf. A109613, A275281, A275283.

Sequence in context: A155197 A147839 A126694 * A264912 A323216 A024091

Adjacent sequences: A305195 A305196 A305197 * A305199 A305200 A305201

Keyword

nonn

Author

Alois P. Heinz, May 27 2018

Status

approved