A059301 Number of filter bases of an n-set.

1, 5, 31, 569, 165211, 12885396101, 64563604303081738807, 1361129467683753854111752846879267953905, 521064401567922879406069432539095585345840013599959430520674634220747299433267

Offset

1,2

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #42.

Links

Harry J. Smith, Table of n, a(n) for n = 1..12

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k)*2^(2^k-1).

a(n) ~ n * 2^(2^(n-1)-1). - Vaclav Kotesovec, Nov 27 2017

Mathematica

Table[Sum[Binomial[n, k]*2^(2^k - 1), {k, 0, n - 1}], {n, 1, 10}] (* G. C. Greubel, Jan 06 2017 *)

Prog

(PARI) { for (n = 1, 12, a=0; for (k=0, n-1, a+=binomial(n, k)*2^(2^k - 1); ); write("b059301.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 25 2009
(PARI) a(n) = sum(k=0, n-1, binomial(n, k)*2^(2^k-1)); \\ Michel Marcus, Jan 03 2016

Crossrefs

Sequence in context: A020514 A201307 A228647 * A225158 A299887 A088548

Adjacent sequences: A059298 A059299 A059300 * A059302 A059303 A059304

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2001

Status

approved