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A229224
The partition function G(n,7).
3
1, 1, 2, 5, 15, 52, 203, 877, 4139, 21137, 115874, 677623, 4204927, 27565188, 190168577, 1376119903, 10414950785, 82230347149, 675762947626, 5768465148493, 51054457464731, 467728049807348, 4428770289719931, 43281554035140829, 436015324638219779
OFFSET
0,3
COMMENTS
Number G(n,7) of set partitions of {1,...,n} into sets of size at most 7.
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..7} x^j/j!).
MAPLE
G:= proc(n, k) option remember; local j; if k>n then G(n, n)
elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
end:
a:= n-> G(n, 7):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n-1, i-1), i=1..min(n, 7)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2016
MATHEMATICA
CoefficientList[Exp[Sum[x^j/j!, {j, 1, 7}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)
CROSSREFS
Column k=7 of A229223.
Cf. A276927.
Sequence in context: A099262 A141081 A108305 * A343668 A276724 A287586
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2013
STATUS
approved