cp's OEIS Frontend

A212700 a(n) = 5*n*6^(n-1).

%I A212700 #28 May 15 2025 01:03:16
%S A212700 5,60,540,4320,32400,233280,1632960,11197440,75582720,503884800,
%T A212700 3325639680,21767823360,141490851840,914248581120,5877312307200,
%U A212700 37614798766080,239794342133760,1523399350026240,9648195883499520,60935974001049600,383896636206612480,2413064570441564160
%N A212700 a(n) = 5*n*6^(n-1).
%C A212700 Main transitions in systems of n particles with spin 5/2.
%C A212700 Refer to the general explanation in A212697.
%C A212700 This particular sequence is obtained for base b=6, corresponding to spin S=(b-1)/2=5/2.
%C A212700 Arithmetic derivative of 6^n: a(n) = A003415(6^n). - _Bruno Berselli_, Oct 22 2013
%H A212700 Stanislav Sykora, <a href="/A212700/b212700.txt">Table of n, a(n) for n = 1..100</a>
%H A212700 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%H A212700 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).
%F A212700 a(n) = n*(b-1)*b^(n-1): for this sequence, set b=6.
%F A212700 From _R. J. Mathar_, Oct 15 2013: (Start)
%F A212700 G.f.: 5*x/(6*x-1)^2.
%F A212700 a(n) = 5*A053469(n). (End)
%F A212700 From _Elmo R. Oliveira_, May 14 2025: (Start)
%F A212700 E.g.f.: 5*x*exp(6*x).
%F A212700 a(n) = A008587(n)*A000400(n-1).
%F A212700 a(n) = 12*a(n-1) - 36*a(n-2) for n > 2. (End)
%t A212700 Rest@ CoefficientList[Series[5 x/(6 x - 1)^2, {x, 0, 18}], x] (* or *)
%t A212700 Array[5 # 6^(# - 1) &, 18] (* _Michael De Vlieger_, Nov 18 2019 *)
%o A212700 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212700 for (n=1, 100, write("b212700.txt", n, " ", mtrans(n, 6)))
%Y A212700 Cf. A001787, A212697, A212698, A212699, A212701, A212702, A212703, A212704 (b = 2, 3, 4, 5, 7, 8, 9, 10).
%Y A212700 Cf. A000400, A003415, A008587, A053469.
%K A212700 nonn,easy
%O A212700 1,1
%A A212700 _Stanislav Sykora_, May 25 2012