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A364267
Total number of blocks in all set partitions of [n] such that each element is contained in a block whose index parity coincides with the parity of the element.
2
0, 1, 2, 5, 9, 24, 55, 169, 454, 1567, 4823, 18422, 63609, 265929, 1014266, 4595861, 19143089, 93286964, 420483103, 2189786125, 10601936382, 58688597511, 303349005967, 1776842374930, 9754696729753, 60223101819493, 349624680839546, 2267363687696309
OFFSET
0,3
COMMENTS
All odd elements are in blocks with an odd index and all even elements are in blocks with an even index. Blocks are ordered with increasing least elements.
LINKS
FORMULA
a(n) = Sum_{k=0..n} k * A274537(n,k).
a(n) mod 2 = A011655(n+1) for n>=1.
EXAMPLE
a(4) = 9 = 2 + 3 + 4: 13|24, 1|24|3, 1|2|3|4.
a(5) = 24 = 2 + 3 + 3 + 3 + 4 + 4 + 5: 135|24, 13|24|5, 15|24|3, 1|24|35, 15|2|3|4, 1|2|35|4, 1|2|3|4|5.
MAPLE
b:= proc(n, m, t) option remember; `if`(n=0, m, add(
`if`(irem(j, 2)=t, b(n-1, max(m, j), 1-t), 0), j=1..m+1))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..30);
CROSSREFS
Sequence in context: A075198 A294633 A320798 * A006405 A305189 A344394
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 16 2023
STATUS
approved