A190529 The number of set partitions of {1,2,...,n} into a prime number of blocks each of which contains a prime number of elements.

3, 10, 25, 126, 336, 694, 3711, 22935, 155628, 789009, 4133207, 26216386, 172746848, 1257901128, 8859163896, 63208414749, 453778734700, 3084827391031, 21322774479601, 144228129141558, 982574515258416, 7457862499069701, 62895482731826525, 635323164540457770

Offset

4,1

Links

Alois P. Heinz, Table of n, a(n) for n = 4..500

Formula

E.g.f.: A(A(x)) where A(x) = Sum_{p=prime} x^p/p!.

Maple

with(combinat): with(numtheory):
b:= proc(n, i, m) option remember; `if`(n=0, `if`(isprime(m), 1, 0),
      `if`(i<1, 0, (p-> add(multinomial(n, n-p*j, p$j)/j!*
       b(n-p*j, i-1, m+j), j=0..n/p))(ithprime(i))))
    end:
a:= n-> b(n, pi(n), 0):
seq(a(n), n=4..30);  # Alois P. Heinz, Sep 17 2015

Mathematica

a= Table[Prime[n], {n, 1, 25}]; b[x_]:= Sum[x^i/i!, {i, a}]; Range[0, 25]! CoefficientList[Series[b[b[x]], {x, 0, 25}], x]

Crossrefs

Sequence in context: A100001 A227937 A299754 * A343584 A335970 A212967

Adjacent sequences: A190526 A190527 A190528 * A190530 A190531 A190532

Keyword

nonn

Author

Geoffrey Critzer, May 11 2011

Status

approved