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A305197 Number of set partitions of [n] with symmetric block size list of length A004525(n). 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 13 2018, from Maple *)

CROSSREFS

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

Cf. A004525, A275281.

Sequence in context: A100702 A224031 A147586 * A071716 A306088 A188625

Adjacent sequences:  A305194 A305195 A305196 * A305198 A305199 A305200

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 27 2018

STATUS

approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)