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A343319
Number of ways to partition n labeled elements into sets of different sizes of at least 4.
3
1, 0, 0, 0, 1, 1, 1, 1, 1, 127, 211, 793, 1288, 3719, 6007, 646439, 1467077, 7211843, 30123763, 91160937, 293184840, 1118980377, 110635063749, 319072758997, 1918239941962, 9518126978941, 58119248603131, 202992067559011, 1031021295578251, 4151156602678042, 650225250329137612
OFFSET
0,10
LINKS
FORMULA
E.g.f.: Product_{k>=4} (1 + x^k/k!).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, b(n, i+1)+b(n-i, i+1)*binomial(n, i)))
end:
a:= n-> b(n, 4):
seq(a(n), n=0..30); # Alois P. Heinz, Apr 28 2021
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 + x^k/k!), {k, 4, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -(n - 1)! Sum[DivisorSum[k, # (-#!)^(-k/#) &, # > 3 &] a[n - k]/(n - k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 28 2021
STATUS
approved