This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307375 #14 Jun 10 2023 19:10:21
%S A307375 1,1,3,17,151,1893,31499,666169,17351967,543441005,20079329875,
%T A307375 861908850561,42439075349543,2371469004695797,149022897087857691,
%U A307375 10448429535366899273,811758520658841809839,69463012765807086749949,6511800419610377560644707,665560984365147223546851985
%N A307375 Expansion of Sum_{j>=0} j!*x^j / Product_{k=1..j} (1 - k^2*x).
%C A307375 a(n) is the number of partitions of [2n] such that the largest element of each block is even. a(3) = 17: 123456, 1234|56, 12356|4, 124|356, 1256|34, 12|3456, 12|34|56, 12|356|4, 13456|2, 134|256, 134|2|56, 1356|24, 1356|2|4, 14|2356, 156|234, 14|2|356, 156|2|34. - _Alois P. Heinz_, Jun 10 2023
%H A307375 Alois P. Heinz, <a href="/A307375/b307375.txt">Table of n, a(n) for n = 0..303</a>
%p A307375 b:= proc(n, x, y) option remember; `if`(n=0, 1, `if`(n::odd, 0,
%p A307375 b(n-1, y, x+1))+b(n-1, y, x)*x+b(n-1, y, x)*y)
%p A307375 end:
%p A307375 a:= n-> b(2*n, 0$2):
%p A307375 seq(a(n), n=0..19); # _Alois P. Heinz_, Jun 10 2023
%t A307375 nmax = 19; CoefficientList[Series[Sum[j! x^j/Product[(1 - k^2 x), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x]
%Y A307375 Cf. A000670, A135920, A229234, A363589.
%Y A307375 Bisection of A290383 (even part).
%K A307375 nonn
%O A307375 0,3
%A A307375 _Ilya Gutkovskiy_, Apr 06 2019