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A190476 The number of partitions of the set {1,2,...,n} into subsets (blocks,cells) having a prime number of elements. 2
1, 0, 1, 1, 3, 11, 25, 127, 441, 1954, 10011, 45266, 264583, 1445380, 8585655, 55660801, 352151073, 2482766225, 17559191557, 129772490863, 1013321885751, 7972553309386, 66428256850935, 564371629663172, 4946383948336009, 45027627776367801, 416996057365437135 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Equivalently, a(n) is the number of equivalence relations on a set of n distinct elements such that each equivalence class contains a prime number of elements.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

E.g.f.: exp(Sum_p=prime,x^p/p!).

MAPLE

with(numtheory):

b:= proc(n, i) option remember; local p;

      if n=0 then 1

    elif n=1 or i<1 then 0

    else p:= ithprime(i);

         b(n, i-1) +add(mul(binomial(n-(h-1)*p, p), h=1..j)

                    *b(n-j*p, i-1)/j! , j=1..iquo(n, p))

      fi

    end:

a:= n-> b(n, pi(n)):

seq(a(n), n=0..30); # Alois P. Heinz, Nov 02 2011

MATHEMATICA

a= Table[Prime[n], {n, 1, 20}];

  b= Sum[x^i/i!, {i, a}];

  Range[0, 20]! CoefficientList[Series[Exp[b], {x, 0, 20}], x]

CROSSREFS

Sequence in context: A184634 A164303 A129082 * A060746 A111935 A175441

Adjacent sequences:  A190473 A190474 A190475 * A190477 A190478 A190479

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, May 10 2011

STATUS

approved

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Last modified November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)