A141014 E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=15.

0, 4, 24, 260, 3528, 51332, 762744, 11406980, 170939688, 2563287812, 38445332184, 576660215300, 8649804864648, 129746582562692, 1946196290656824, 29192932133689220, 437893920912786408

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, -158, 360, -225).

Programs

Magma

[0] cat [1+3^(n-1)+5^(n-1)+15^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 13 2012

Maple

A141014 := proc(n) local d; add(d^(n-1),d=numtheory[divisors](15)) ; end proc: seq(A141014(n),n=1..20) ; # R. J. Mathar, Mar 05 2010

Mathematica

CoefficientList[Series[-4 x (-1 + 18 x - 79 x^2 + 90 x^3)/((x-1) (15 x-1) (3 x-1) (5 x-1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2012 *)
LinearRecurrence[{24,-158,360,-225},{0,4,24,260,3528},20] (* Harvey P. Dale, May 18 2023 *)

Formula

a(n) = sum_{d|15} d^(n-1) = 1+3^(n-1)+5^(n-1)+15^(n-1). G.f.: -4*x*(-1+18*x-79*x^2+90*x^3)/((x-1) * (15*x-1) * (3*x-1) * (5*x-1)). a(n) = 24*a(n-1) -158*a(n-2) +360*a(n-3) -225*a(n-4). - R. J. Mathar, Mar 05 2010

a(n) = A034472(n-1)*A034474(n-1). - R. J. Mathar, May 26 2016