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a(n) = 24*A274300(n) + 14.
1

%I #15 May 27 2024 07:14:49

%S 38,38,38,134,326,326,326,1862,1862,8006,20294,44870,94022,192326,

%T 192326,585542,1371974,2944838,2944838

%N a(n) = 24*A274300(n) + 14.

%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.)

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

%Y Cf. A000587, A274300.

%K nonn,more

%O 0,1

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