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A202477 The number of ways to build all endofunctions on each block of every set partition of {1,2,...,n}. 2
1, 1, 5, 40, 437, 6036, 100657, 1965160, 43937385, 1106488720, 30982333661, 954607270464, 32090625710365, 1168646120904640, 45826588690845705, 1924996299465966976, 86231288506425806033, 4103067277186778016000, 206655307175847710248885 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..385

FORMULA

E.g.f.: exp(T(x)/(1-T(x))) where T(x) is the e.g.f. for A000169.

a(n) ~ n^(n-1/3) * exp(3/2*n^(1/3) - 2/3) / sqrt(3). - Vaclav Kotesovec, Sep 24 2013

MAPLE

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1,

      `if`(i<1, 0, add(i^(i*j)*b(n-i*j, i-1)*

       multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..20);  # Alois P. Heinz, Mar 29 2016

MATHEMATICA

nn = 20; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}] ;

Range[0, nn]! CoefficientList[Series[Exp[t/(1 - t)], {x, 0, nn}], x]

CROSSREFS

Cf. A000262 (the same for permutations).

Sequence in context: A290932 A258172 A304866 * A034000 A000359 A121886

Adjacent sequences:  A202474 A202475 A202476 * A202478 A202479 A202480

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Dec 19 2011

STATUS

approved

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Last modified August 6 09:02 EDT 2020. Contains 336228 sequences. (Running on oeis4.)