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%I #8 Sep 13 2024 17:49:20
%S 1,6,19,100,1053,15666,279991,5764872,134217817,3486784510,
%T 100000000131,3138428376876,106993205379253,3937376385699498,
%U 155568095557812463,6568408355712890896,295147905179352826161,14063084452067724991350,708235345355337676358011,37589973457545958193356020,2097152000000000000000000461
%N a(n) = (n+(n+1)) + (n*(n+1)) + (n^(n+1)).
%C Sum of three arithmetic operations (sum, product, powers) of two consecutive integers.
%F a(n) = A028387(n) + A007778(n). - _R. J. Mathar_, Apr 03 2008
%e a(0) = (0+1) + (0*1) + (0^1) = 1;
%e a(1) = (1+2) + (1*2) + (1^2) = 6;
%e a(2) = (2+3) + (2*3) + (2^3) = 19; etc.
%p A028387 := proc(n) n+(n+1)^2 ; end: A007778 := proc(n) n^(n+1) ; end: A138748 := proc(n) A028387(n)+A007778(n) ; end: seq(A138748(n),n=0..20) ; # _R. J. Mathar_, Apr 03 2008
%t Table[2n+1+n(n+1)+n^(n+1),{n,0,20}] (* _Harvey P. Dale_, Sep 13 2024 *)
%K easy,nonn
%O 0,2
%A _Anthony J. DeFusco II_, Mar 28 2008
%E More terms from _R. J. Mathar_, Apr 03 2008