Search: id:A007781
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%I A007781
%S A007781 1,3,23,229,2869,43531,776887,15953673,370643273,9612579511,
%T A007781 275311670611,8630788777645,293959006143997,10809131718965763,
%U A007781 426781883555301359,18008850183328692241,808793517812627212561
%N A007781 (n+1)^(n+1) - n^n.
%C A007781 a(n)=A000312(n)-A000312(n-1).
%C A007781 (12n^2 + 6n + 1)^2 divides a(6n+1), where (12n^2 + 6n + 1) = (2n+1)^3 
               - (2n)^3{19,61,127,217,331,469,631,817,1027,1261,...} = A127854(n) 
               = A003215(2n) are the hex (or centered hexagonal) numbers. The prime 
               numbers of the form (12n^2 + 6n + 1) belong to A002407 Cuban primes: 
               primes of the form p = (x^3 - y^3 )/(x - y), x=y+1 (prime hex numbers). 
               - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 09 2007
%D A007781 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               equation (6.7).
%H A007781 R. K. Hoeflin, <a href="http://www.eskimo.com/~miyaguch/mega.html">Mega 
               Test</a>
%H A007781 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerDifferencePrime.html">Power Difference Prime</a>
%F A007781 |disc(x^(n+1)-x+1)|.
%e A007781 a(14) = 10809131718965763 = 3 * 61^2 * 968299894201.
%t A007781 a[n_]:=(n+1)^(n+1)-n^n; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 11 2008]
%Y A007781 Cf. A068954, A068955, A068956, A068957, A068146.
%Y A007781 Cf. A127854 = Largest number k such that k^2 divides A007781(6n+1). Cf. 
               A003215, A002407.
%Y A007781 Sequence in context: A068954 A068955 A151393 this_sequence A068146 A162591 
               A122009
%Y A007781 Adjacent sequences: A007778 A007779 A007780 this_sequence A007782 A007783 
               A007784
%K A007781 nonn
%O A007781 0,2
%A A007781 peter.mccormack(AT)its.csiro.au

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