A000314 -id:A000314 - cp's OEIS frontend

A035356 Number of asymmetric polygonal cacti with bridges (mixed Husimi trees).

1, 1, 0, 0, 0, 0, 1, 4, 13, 45, 143, 461, 1470, 4747, 15364, 50283, 165549, 549734, 1837539, 6184589, 20938983, 71297174, 244009225, 839101403, 2898145437, 10050549437, 34985611467, 122209803101, 428285696895, 1505491979826

Offset: 0

Christian G. Bower, Nov 15 1998

nonn

Cf. A000083, A000237, A000314, A035082, A035349-A035357.

G.f.: A(x) = B(x) + C(x) - B(x)*D(x), where B, C, D respectively are g.f.s of A035353, A035354, A035355.

A359276 a(n) = greatest integer k such that (n+k)! <= n^n.

Original entry on oeis.org

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16

Offset: 1

Clark Kimberling, Jan 26 2023

nonn

Cf. A000142, A000314.

a[n_] := Select[-1 + Range[1300], (n + #)! <= n^n < (n + # + 1)! &]
Flatten[Table[a[n], {n, 1, 200}]]

cp's OEIS Frontend

A035356 Number of asymmetric polygonal cacti with bridges (mixed Husimi trees).

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A359276 a(n) = greatest integer k such that (n+k)! <= n^n.

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Mathematica