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A307375
Expansion of Sum_{j>=0} j!*x^j / Product_{k=1..j} (1 - k^2*x).
3
1, 1, 3, 17, 151, 1893, 31499, 666169, 17351967, 543441005, 20079329875, 861908850561, 42439075349543, 2371469004695797, 149022897087857691, 10448429535366899273, 811758520658841809839, 69463012765807086749949, 6511800419610377560644707, 665560984365147223546851985
OFFSET
0,3
COMMENTS
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
LINKS
MAPLE
b:= proc(n, x, y) option remember; `if`(n=0, 1, `if`(n::odd, 0,
b(n-1, y, x+1))+b(n-1, y, x)*x+b(n-1, y, x)*y)
end:
a:= n-> b(2*n, 0$2):
seq(a(n), n=0..19); # Alois P. Heinz, Jun 10 2023
MATHEMATICA
nmax = 19; CoefficientList[Series[Sum[j! x^j/Product[(1 - k^2 x), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
Bisection of A290383 (even part).
Sequence in context: A303063 A209305 A182957 * A007767 A075820 A145081
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2019
STATUS
approved