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A363589 Number of partitions of [2n+1] such that the largest element of each block is odd.

%I A363589 #13 Jun 12 2023 17:22:45
%S A363589 1,2,8,56,584,8360,155720,3633704,103284296,3499082408,138860069192,
%T A363589 6364334129192,332934707138888,19681714722718376,1303617735072968264,
%U A363589 96028608749005335080,7816178772774327523400,698943538498179895072424,68316963055524325115842376
%N A363589 Number of partitions of [2n+1] such that the largest element of each block is odd.
%H A363589 Alois P. Heinz, <a href="/A363589/b363589.txt">Table of n, a(n) for n = 0..303</a>
%H A363589 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A363589 a(n) = A290383(2*n+1).
%e A363589 a(0) = 1: 1.
%e A363589 a(1) = 2: 123, 1|23.
%e A363589 a(2) = 8: 12345, 123|45, 1245|3, 13|245, 145|23, 1|2345, 1|23|45, 1|245|3.
%p A363589 b:= proc(n, x, y) option remember; `if`(n=0, 1, `if`(n::even, 0,
%p A363589       b(n-1, y, x+1))+b(n-1, y, x)*x+b(n-1, y, x)*y)
%p A363589     end:
%p A363589 a:= n-> b(2*n+1, 0$2):
%p A363589 seq(a(n), n=0..20);
%Y A363589 Bisection of A290383 (odd part).
%Y A363589 Cf. A000110, A307375 (the largest element of each block is even).
%K A363589 nonn
%O A363589 0,2
%A A363589 _Alois P. Heinz_, Jun 10 2023