A274300 - OEIS

%I #16 May 27 2024 07:14:45

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

%T 122701,122701

%N Arises in study of A000587.

%H Tewodros Amdeberhan, Valerio De Angelis, and Victor H. Moll, <a href="https://doi.org/10.1007/978-3-642-30979-3_2">Complementary Bell numbers: Arithmetical properties and Wilf's conjecture</a>, 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; <a href="https://www.researchgate.net/publication/240810169_Complementary_Bell_numbers">ResearchGate link</a>.

%H Valerio De Angelis and Dominic Marcello, <a href="https://doi.org/10.4169/amer.math.monthly.123.6.557">Wilf's conjecture</a>, The American Mathematical Monthly, Vol. 123, No. 6 (2016), pp. 557-573; <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.557">alternative link</a>; <a href="https://www.researchgate.net/profile/Valerio-De-Angelis/publication/303883766_Wilf&#39;s_Conjecture">ResearchGate link</a>. (Note a(14) has a typo.)

%F 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

%t 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 *)

%Y Cf. A000587, A007814, A274301.

%K nonn,more

%O 0,4

%A _N. J. A. Sloane_, Jun 20 2016