A016164 Expansion of 1/((1-5*x)*(1-10*x)).

1, 15, 175, 1875, 19375, 196875, 1984375, 19921875, 199609375, 1998046875, 19990234375, 199951171875, 1999755859375, 19998779296875, 199993896484375, 1999969482421875, 19999847412109375, 199999237060546875

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..994

Index entries for linear recurrences with constant coefficients, signature (15,-50).

Formula

a(n) = (5^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).

a(n) = -5^n + 2*10^n.

G.f.: 1/((1-5*x)*(1-10*x)).

E.g.f.: (d^2/dx^2)((((exp(5*x)-1)/5)^2)/2!) = -exp(5*x) + 2*exp(10*x).

Sum_{k=1..n} 5^(k-1)*5^(n-k)*binomial(n, k). - Zerinvary Lajos, Sep 24 2006

a(0)=1, a(n) = 10*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011

Mathematica

Table[5^n*(2^(n+1)-1), {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{15, -50}, {1, 15}, 20] (* Harvey P. Dale, Aug 08 2023 *)

Prog

(PARI) Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012
(Magma) [n le 2 select 15^(n-1) else 15*Self(n-1) -50*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 09 2024
(SageMath)
A016164=BinaryRecurrenceSequence(15, -50, 1, 15)
[A016164(n) for n in range(31)] # G. C. Greubel, Nov 09 2024

Crossrefs

Second column of triangle A075500.

Cf. A008277, A016161, A075911.

Sequence in context: A036083 A346320 A051588 * A354135 A354137 A380370

Adjacent sequences: A016161 A016162 A016163 * A016165 A016166 A016167

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved