A343319 Number of ways to partition n labeled elements into sets of different sizes of at least 4.

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

Alois P. Heinz, Table of n, a(n) for n = 0..700

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}]

Crossrefs

Cf. A007837, A025149, A032311, A057837, A232475, A341283, A343542.

Sequence in context: A095730 A325078 A276261 * A045117 A178700 A142466

Adjacent sequences: A343316 A343317 A343318 * A343320 A343321 A343322

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 28 2021

Status

approved