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A363511 Number of partitions of [n] having exactly one parity change within their blocks.

%I A363511 #10 Jun 06 2023 20:00:20
%S A363511 0,0,1,2,6,18,61,210,778,3008,12219,52268,231726,1083012,5202199,
%T A363511 26307710,135972580,738339310,4081523615,23649300862,139096468520,
%U A363511 855529383396,5329630673249,34643027568520,227682351175868,1558106351450416,10766192988109009
%N A363511 Number of partitions of [n] having exactly one parity change within their blocks.
%H A363511 Alois P. Heinz, <a href="/A363511/b363511.txt">Table of n, a(n) for n = 0..500</a>
%H A363511 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A363511 a(4) = 6: 124|3, 12|3|4, 134|2, 1|23|4, 14|2|3, 1|2|34.
%p A363511 b:= proc(n, x, y) option remember; convert(series(
%p A363511      `if`(n=0, 1, `if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z))
%p A363511        +b(n-1, y, x)*x + b(n-1, y, x+1)), z, 2), polynom)
%p A363511     end:
%p A363511 a:= n-> coeff(b(n, 0$2), z, 1):
%p A363511 seq(a(n), n=0..27);
%Y A363511 Column k=1 of A363493.
%Y A363511 Cf. A000110, A124419.
%K A363511 nonn
%O A363511 0,4
%A A363511 _Alois P. Heinz_, Jun 06 2023