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%I #33 Sep 08 2022 08:45:14
%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
%H Vincenzo Librandi, <a href="/A097809/b097809.txt">Table of n, a(n) for n = 0..1000</a>
%H Tamas Lengyel, <a href="https://doi.org/10.1016/j.jnt.2014.09.015">On p-adic properties of the Stirling numbers of the first kind</a>, Journal of Number Theory, 148 (2015) 73-94.
%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(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3), with a(0)=1, a(1)=4, a(2)=12.
%F E.g.f.: 5*exp(2*x) - 2*(2+x)*exp(x). - _G. C. Greubel_, Dec 30 2021
%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
%o (Sage) [5*2^n -2*(n+2) for n in (0..30)] # _G. C. Greubel_, Dec 30 2021
%Y Cf. A079583, A097810.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Aug 25 2004
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