cp's OEIS Frontend

A084901 a(n) = 4^(n-2)*n*(5*n+3)/2.

%I A084901 #26 Jun 01 2025 22:15:03
%S A084901 0,1,13,108,736,4480,25344,136192,704512,3538944,17367040,83623936,
%T A084901 396361728,1853882368,8573157376,39258685440,178241142784,
%U A084901 803158884352,3594887626752,15994458210304,70781061038080,311711546474496
%N A084901 a(n) = 4^(n-2)*n*(5*n+3)/2.
%C A084901 Binomial transform of A084900. Third binomial transform of heptagonal numbers A000566. Fourth binomial transform of (0,1,5,0,0,0,...).
%C A084901 Coefficients in the hypergeometric series identity 1 - 13*x/(x + 12) + 108*x*(x - 1)/((x + 12)*(x + 16)) - 736*x*(x - 1)*(x - 2)/((x + 12)*(x + 16)*(x + 20)) + ... = 0, valid in the half-plane Re(x) > 0. Cf. A276289 and A077616. - _Peter Bala_, May 30 2019
%H A084901 G. C. Greubel, <a href="/A084901/b084901.txt">Table of n, a(n) for n = 0..1000</a>
%H A084901 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).
%F A084901 G.f.: x*(1+x)/(1-4*x)^3.
%F A084901 E.g.f.: x*(2 + 5*x)*exp(4*x)/2. - _G. C. Greubel_, Jun 06 2019
%F A084901 a(n) = 12*a(n-1)-48*a(n-2)+64*a(n-3). - _Wesley Ivan Hurt_, May 28 2021
%t A084901 Table[2^(2*n-5)*n*(5*n+3), {n,0,30}] (* _G. C. Greubel_, Jun 06 2019 *)
%t A084901 LinearRecurrence[{12,-48,64},{0,1,13},30] (* or *) CoefficientList[ Series[-((x (1+x))/(-1+4 x)^3),{x,0,30}],x] (* _Harvey P. Dale_, Jul 14 2021 *)
%o A084901 (PARI) vector(30, n, n--; 2^(2*n-5)*n*(5*n+3)) \\ _G. C. Greubel_, Jun 06 2019
%o A084901 (Magma) [2^(2*n-5)*n*(5*n+3): n in [0..30]]; // _G. C. Greubel_, Jun 06 2019
%o A084901 (Sage) [2^(2*n-5)*n*(5*n+3) for n in (0..30)] # _G. C. Greubel_, Jun 06 2019
%o A084901 (GAP) List([0..30], n-> 2^(2*n-5)*n*(5*n+3)); # _G. C. Greubel_, Jun 06 2019
%Y A084901 Cf. A084902, A077616, A276289.
%K A084901 easy,nonn
%O A084901 0,3
%A A084901 _Paul Barry_, Jun 10 2003