A161159 a(n) = A003739(n)/(5*A001906(n)*A006238(n)).

9, 245, 7776, 254035, 8336079, 273725760, 8988999201, 295197803645, 9694285226784, 318360072624475, 10454936893196391, 343339870595441280, 11275272921720374649, 370279686003420394565, 12159975800265309667296

Offset: 1

Author

R. J. Mathar, Jun 03 2009

Keywords

• nonn
• easy

Comments

Proposed by R. Guy in the seqfan list, Mar 28 2009.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..600
• Index entries for linear recurrences with constant coefficients, signature (40,-248,430,-248,40,-1).

Programs

Magma

I:=[9,245,7776,254035,8336079,273725760]; [n le 6 select I[n] else 40*Self(n-1)-248*Self(n-2)+430*Self(n-3)-248*Self(n-4)+40*Self(n-5)-Self(n-6): n in [1..16]]; // Vincenzo Librandi, Dec 19 2012

Maple

seq(coeff(series(x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3+x^4)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Dec 25 2019

Mathematica

CoefficientList[Series[(9-115x+208x^2-115x^3+9x^4)/((1-5x+x^2)*(1-35x+72x^2- 35x^3+x^4)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 19 2012 *)

PARI

my(x='x+O('x^30)); Vec(x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+ x^2)*(1-35*x+72*x^2-35*x^3+x^4))) \\ G. C. Greubel, Dec 25 2019

Sage

def A161159_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3+x^4)) ).list()
a=A161159_list(30); a[1:] # G. C. Greubel, Dec 25 2019

Formula

a(n) = 40*a(n-1) -248*a(n-2) +430*a(n-3) -248*a(n-4) +40*a(n-5) -a(n-6).

G.f.: x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3 +x^4)).