A332248 Number of set partitions of [n] where all prime-indexed blocks are not singletons.

1, 1, 1, 2, 5, 15, 60, 286, 1423, 7185, 37758, 212596, 1293577, 8415869, 57715274, 414520958, 3125102795, 24880061105, 209909409566, 1871945790360, 17503956383037, 169851122851049, 1694189515772750, 17248694322541778, 178473482993477591, 1873036127628583885

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Example

a(1) = 1: 1.
a(2) = 1: 12.
a(3) = 2: 123, 1|23.
a(4) = 5: 1234, 12|34, 13|24, 14|23, 1|234.
a(5) = 15: 12345, 123|45, 124|35, 125|34, 12|345, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345, 1|23|45, 1|24|35, 1|25|34.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, add(b(n-j, i+1)*
       binomial(n-1, j-1), j=`if`(isprime(i), 2, 1)..n))
    end:
a:= n-> b(n, 1):
seq(a(n), n=0..32);

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, Sum[b[n-j, i+1] Binomial[n-1, j-1], {j, If[PrimeQ[i], 2, 1], n}]];
a[n_] := b[n, 1];
a /@ Range[0, 32] (* Jean-François Alcover, May 08 2020, after Maple *)

Crossrefs

Cf. A000040, A000110, A000296, A332398.

Sequence in context: A208808 A266682 A325575 * A030934 A030922 A030916

Adjacent sequences: A332245 A332246 A332247 * A332249 A332250 A332251

Keyword

nonn

Author

Alois P. Heinz, Feb 12 2020

Status

approved