A081042 - OEIS

%I #20 Sep 08 2022 08:45:09

%S 1,13,133,1225,10633,88837,722701,5764801,45294865,351652861,

%T 2703691669,20620693177,156208812697,1176509412085,8816899947037,

%U 65787638066353,488998835524129,3622389432086509,26752509108528805,197038045347164329

%N 7th binomial transform of (1,6,0,0,0,0,0,0,...).

%H Vincenzo Librandi, <a href="/A081042/b081042.txt">Table of n, a(n) for n = 0..300</a>

%H Silvana Ramaj, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=3464&amp;context=etd">New Results on Cyclic Compositions and Multicompositions</a>, Master's Thesis, Georgia Southern Univ., 2021. See p. 67.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49).

%F a(n) = 14*a(n-1) - 49*a(n-2) for n>1, a(0)=1, a(1)=13.

%F a(n) = (6*n+7)*7^(n-1).

%F a(n) = Sum_{k=0..n} (k+1)*6^k*binomial(n, k).

%F G.f.: (1-x)/(1-7*x)^2.

%t CoefficientList[Series[(1 - x)/(1 - 7 x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)

%t LinearRecurrence[{14,-49},{1,13},20] (* _Harvey P. Dale_, Jan 24 2014 *)

%o (Magma) [(6*n+7)*7^(n-1): n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013

%Y Cf. A081041, A081042.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Mar 04 2003