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a(n) = a(n-1)*2^n + 1 where a(0)=1.
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%I #32 Mar 23 2024 19:15:29

%S 1,3,13,105,1681,53793,3442753,440672385,112812130561,57759810847233,

%T 59146046307566593,121131102837896382465,496152997224023582576641,

%U 4064485353259201188467843073,66592528027798752271857140908033,2182103958414909514444214793274425345

%N a(n) = a(n-1)*2^n + 1 where a(0)=1.

%C Also, number of nodes in an n-ary tree with increasing fanout as the level increases. - _Dhruv Matani_, Apr 12 2012

%F a(n) = floor(D*2^(n*(n+1)/2)) where D is a constant, D=1.64163256065515386629... = Sum_{k>=0} 1/2^(k(k+1)/2) = A299998. - _Benoit Cloitre_, Sep 01 2002

%t a = 1; Table[a = a*2^n + 1, {n, 14}] (* _Jayanta Basu_, Jul 02 2013 *)

%o (UBASIC)

%o 25 A=1

%o 30 for I=1 to 20

%o 40 A=A*2^I+1

%o 50 print A

%o 60 next

%o 70 end

%Y Cf. A000225 (nodes in a binary tree).

%Y Cf. A006125, A117261, A299998.

%K easy,nonn

%O 0,2

%A _Felice Russo_, Aug 28 2002

%E Added a(0)=1. Added information from duplicate sequence A182104. - _N. J. A. Sloane_, Dec 28 2015