%I M5239 #32 Sep 12 2022 04:51:58

%S 1,33,155,427,909,1661,2743,4215,6137,8569,11571,15203,19525,24597,

%T 30479,37231,44913,53585,63307,74139,86141,99373,113895,129767,147049,

%U 165801,186083,207955,231477,256709,283711,312543,343265,375937,410619,447371,486253,527325

%N Centered dodecahedral numbers.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A005904/b005904.txt">Table of n, a(n) for n = 0..10000</a>

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.

%H Boon K. Teo and N. J. A. Sloane, <a href="https://doi.org/10.1021/ic00220a025">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558; <a href="http://neilsloane.com/doc/Me117.pdf">alternative link</a>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (2*n+1)*(5*n^2+5*n+1).

%F Sum_{n>=0} 1/a(n) = -psi((5+sqrt(5))/10) - psi((5-sqrt(5))/10) - 2*gamma - 4*log(2), where psi is the digamma function and gamma is Euler's constant (A001620). - _Amiram Eldar_, Sep 12 2022

%p A005904:=(z+1)*(z**2+28*z+1)/(z-1)**4; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%t a[n_] := (2*n + 1) * (5*n^2 + 5*n + 1); Array[a, 30, 0] (* _Amiram Eldar_, Sep 12 2022 *)

%Y Cf. A001620, A006566.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.