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URL: https://oeis.org/A393570

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A393570
Number of ordered set partitions of [n] with palindromic block sizes.
2
1, 1, 3, 7, 43, 171, 1581, 8793, 108347, 774763, 11933593, 104297733, 1927782517, 19911877285, 429380343003, 5117339645967, 126114825517467, 1703436268264475, 47228082430915401, 712959300038464773, 21963252371434460273, 366460163952069281073, 12417991841852814383103
OFFSET
0,3
LINKS
FORMULA
E.g.f.: exp(x)/(1 - Sum_{i>0} x^(2*i)/(i!)^2).
EXAMPLE
The ordered set partition of [5], 25|4|13 has block sizes 2,1,2 so it is counted under a(5) = 171.
a(3) = 7: 1|2|3, 1|3|2, 2|1|3, 2|3|1, 3|1|2, 3|2|1, 123.
MAPLE
a:= proc(n) option remember; 1+add(a(n-2*j)*
combinat[multinomial](n, n-2*j, j$2), j=1..n/2)
end:
seq(a(n), n=0..22); # Alois P. Heinz, Mar 01 2026
PROG
(PARI) C_x(N) = {my(x='x+O('x^(N+1))); Vec(serlaplace( exp(x)/(1- sum(i=1, N, x^(2*i)/(i!)^2))))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Tyler Rascoe, Feb 21 2026
STATUS
approved