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A097809 a(n) = 5*2^n-2*n-4. 3

%I

%S 1,4,12,30,68,146,304,622,1260,2538,5096,10214,20452,40930,81888,

%T 163806,327644,655322,1310680,2621398,5242836,10485714,20971472,

%U 41942990,83886028,167772106,335544264,671088582,1342177220,2684354498

%N a(n) = 5*2^n-2*n-4.

%C Rows sums of the infinite triangle defined by T(n,n)=1, T(n,0)=n*(n+1)+1 for n=0, 1, 2, ... and interior terms defined by the Pascal-type recurrence T(n,k) = T(n-1,k-1) +T(n-1,k): sum_{k=0..n} T(n,k) = a(n). T is apparently obtained by deleting the first two columns of A129687. - _J. M. Bergot_, Feb 23 2013

%D Tamas Lengyel, On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory, 148 (2015) 73-94.

%H Vincenzo Librandi, <a href="/A097809/b097809.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).

%F G.f.: (1+x^2)/((1-x)^2*(1-2*x)).

%F a(n) = 2*a(n-1)+2*n, n>0.

%F a(0)=1, a(1)=4, a(2)=12, a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3).

%t s=1;lst={s};Do[s+=(s+=n);AppendTo[lst, s], {n, 4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 11 2008 *)

%t LinearRecurrence[{4,-5,2},{1,4,12},30] (* _Harvey P. Dale_, Oct 11 2018 *)

%o (MAGMA) [5*2^n-2*n-4: n in [0..30]]; // _Vincenzo Librandi_, Feb 24 2013

%Y Cf. A079583, A097810.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Aug 25 2004

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)