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
Links
- 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.)
Programs
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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 *)
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