A274300 Arises in study of A000587.

1, 1, 1, 5, 13, 13, 13, 77, 77, 333, 845, 1869, 3917, 8013, 8013, 24397, 57165, 122701, 122701

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Tewodros Amdeberhan, Valerio De Angelis, and Victor H. Moll, Complementary Bell numbers: Arithmetical properties and Wilf's conjecture, in: I. Kotsireas and E. Zima (eds.), Advances in Combinatorics: Waterloo Workshop in Computer Algebra, W80, May 26-29, 2011, Springer Berlin Heidelberg, 2013, pp. 23-56; ResearchGate link.

Valerio De Angelis and Dominic Marcello, Wilf's conjecture, The American Mathematical Monthly, Vol. 123, No. 6 (2016), pp. 557-573; alternative link; ResearchGate link. (Note a(14) has a typo.)

Formula

a(0) = 1; a(n) = a(n-1), if A007814(A000587(24*a(n-1)+14)) > n+4, and a(n-1) + 2^(n-1) otherwise. - Amiram Eldar, May 27 2024

Mathematica

a[0] = 1; a[n_] := a[n] = a[n-1] + If[IntegerExponent[BellB[24*a[n-1] + 14, -1], 2] > n + 4, 0, 2^(n-1)]; Array[a, 11, 0] (* Amiram Eldar, May 27 2024 *)

Crossrefs

Cf. A000587, A007814, A274301.

Sequence in context: A130502 A320814 A274302 * A051899 A085956 A232610

Adjacent sequences: A274297 A274298 A274299 * A274301 A274302 A274303

Keyword

nonn,more

Author

N. J. A. Sloane, Jun 20 2016

Status

approved