A141013 E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=14.

0, 4, 24, 250, 3096, 40834, 554664, 7647250, 106237176, 1481554114, 20701400904, 289537131250, 4051542498456, 56707753666594, 793811662272744, 11112685048647250, 155572843119354936

Offset: 0

Author

R. J. Mathar, Jul 11 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..800
• Index entries for linear recurrences with constant coefficients, signature (24, -163, 336, -196).

Crossrefs

Cf. A141012 (M=13), A141014 (M=15).

Programs

Magma

[0] cat [1+2^(n-1)+7^(n-1)+14^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 12 2012

Maple

A141013 := proc(n) local d; add(d^(n-1),d=numtheory[divisors](14)) ; end proc: seq(A141013(n),n=1..20) ; # R. J. Mathar, Mar 05 2010

Mathematica

CoefficientList[Series[- 2 x (-2 + 36 x - 163 x^2 + 168 x^3)/((x-1) (14*x-1) (2*x-1) (7*x-1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)

Formula

From R. J. Mathar, Mar 05 2010: (Start)

a(n) = sum_{d|14} d^(n-1) = 1+2^(n-1)+7^(n-1)+14^(n-1).

a(n)= 24*a(n-1) -163*a(n-2) +336*a(n-3) -196*a(n-4), n>4.

G.f: -2*x*(-2+36*x-163*x^2+168*x^3)/((x-1)*(14*x-1)*(2*x-1)*(7*x-1)).

(End)

a(n) = A000051(n-1)*A034491(n-1). - R. J. Mathar, May 26 2016