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

5, 60, 540, 4320, 32400, 233280, 1632960, 11197440, 75582720, 503884800, 3325639680, 21767823360, 141490851840, 914248581120, 5877312307200, 37614798766080, 239794342133760, 1523399350026240, 9648195883499520, 60935974001049600, 383896636206612480, 2413064570441564160

Offset: 1

Author

Stanislav Sykora, May 25 2012

Keywords

• nonn
• easy

Comments

Main transitions in systems of n particles with spin 5/2.

Refer to the general explanation in A212697.

This particular sequence is obtained for base b=6, corresponding to spin S=(b-1)/2=5/2.

Arithmetic derivative of 6^n: a(n) = A003415(6^n). - Bruno Berselli, Oct 22 2013

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..100
• Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
• Index entries for linear recurrences with constant coefficients, signature (12,-36).

Crossrefs

Cf. A001787, A212697, A212698, A212699, A212701, A212702, A212703, A212704 (b = 2, 3, 4, 5, 7, 8, 9, 10).

Cf. A000400, A003415, A008587, A053469.

Programs

Mathematica

Rest@ CoefficientList[Series[5 x/(6 x - 1)^2, {x, 0, 18}], x] (* or *)
Array[5 # 6^(# - 1) &, 18] (* Michael De Vlieger, Nov 18 2019 *)

PARI

mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212700.txt", n, " ", mtrans(n, 6)))

Formula

a(n) = n*(b-1)*b^(n-1): for this sequence, set b=6.

From R. J. Mathar, Oct 15 2013: (Start)

G.f.: 5*x/(6*x-1)^2.

a(n) = 5*A053469(n). (End)

From Elmo R. Oliveira, May 14 2025: (Start)

E.g.f.: 5*x*exp(6*x).

a(n) = A008587(n)*A000400(n-1).

a(n) = 12*a(n-1) - 36*a(n-2) for n > 2. (End)