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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..994
- Index entries for linear recurrences with constant coefficients, signature (15,-50).
Programs
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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
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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 *) -
PARI
Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012
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SageMath
A016164=BinaryRecurrenceSequence(15,-50,1,15) [A016164(n) for n in range(31)] # G. C. Greubel, Nov 09 2024
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