A305198 - OEIS

%I #9 Dec 08 2020 08:04:11

%S 1,1,7,56,470,10299,91925,3939653,36298007,2571177913,24158837489,

%T 2557117944391,24350208829581,3601150175699409,34626777577615921,

%U 6820331445080882282,66066554102006208712,16719951521837764142510,162903256982698962545956

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

%H Alois P. Heinz, <a href="/A305198/b305198.txt">Table of n, a(n) for n = 0..200</a>

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

%p b:= proc(n, s) option remember; expand(`if`(n>s,

%p       binomial(n-1, n-s-1)*x, 1)+add(binomial(n-1, j-1)*

%p       b(n-j, s+j)*binomial(s+j-1, j-1), j=1..(n-s)/2)*x^2)

%p     end:

%p a:= n-> coeff(b(2*n+1, 0), x, n+irem(n+1, 2)):

%p seq(a(n), n=0..20);

%t 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];

%t a[n_] := Coefficient[b[2n + 1, 0], x, n + Mod[n + 1, 2]];

%t a /@ Range[0, 20] (* _Jean-François Alcover_, Dec 08 2020, after _Alois P. Heinz_ *)

%Y Bisection (odd part) of A305197.

%Y Cf. A109613, A275281, A275283.

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 27 2018