Search: id:A091344
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%I A091344
%S A091344 0,1,7,31,115,391,1267,3991,12355,37831,115027,348151,1050595,3164071,
%T A091344 9516787,28599511,85896835,257887111,774054547,2322950071,6970423075,
%U A091344 20914414951,62749536307,188261191831,564808741315,1694476555591
%N A091344 a(n) = 2*3^n-3*2^n+1.
%C A091344 Starting with offset 1 = binomial transform of A068193: (1, 6, 18, 42, 
               90,...) and double binomial transform of (1, 5, 7, 5, 7, 5,...). 
               [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009]
%D A091344 Ballot, Christian and Luca, Florian, Prime factors of a^f(n)-1 with an 
               irreducible polynomial f(x). New York J. Math. 12 (2006), 39-45 (electronic).
%D A091344 Ballot, Christian and Luca, Florian, Common prime factors of a^n-b and 
               c^n-d. Unif. Distrib. Theory 2 (2007), no. 2, 19-34 (electronic).
%H A091344 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A091344 a(n)=Sum(i!*i^2*Stirling2(n,i)*(-1)^(n-i), i=1,..,n)
%F A091344 a_n = 6a_{n-1} - 11a_{n-2} + 6a_{n-3}, g.f.: x(1+x)/(1-x)(2-x)(3-x)). 
               - Christian Ballot via R. K. Guy, Jan 13 2009
%p A091344 a:=n->sum((3^(n-j-1)-2^(n-2-j))*12, j=0..n): seq(a(n), n=-1..24); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Feb 11 2007
%p A091344 with (combinat):a:=n->stirling2(n,3)+stirling2(n+1,3): seq(a(n), n=1..26); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
%t A091344 Table[Sum[i!i^2 StirlingS2[n, i](-1)^(n - i), {i, 1, n}], {n, 0, 30}]
%Y A091344 A068293 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009]
%Y A091344 Sequence in context: A055580 A097786 A006458 this_sequence A032197 A114289 
               A147597
%Y A091344 Adjacent sequences: A091341 A091342 A091343 this_sequence A091345 A091346 
               A091347
%K A091344 easy,nonn
%O A091344 0,3
%A A091344 Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004
%E A091344 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 13 2009 at 
               the suggestion of R. K. Guy. The concise definition was provided 
               by Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 01 2004.

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