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A016164 Expansion of 1/((1-5x)(1-10x)). 7
1, 15, 175, 1875, 19375, 196875, 1984375, 19921875, 199609375, 1998046875, 19990234375, 199951171875, 1999755859375, 19998779296875, 199993896484375, 1999969482421875, 19999847412109375, 199999237060546875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

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

Join[{a=1, b=15}, Table[c=15*b-50*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)

PROG

(PARI) Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

CROSSREFS

Second column of triangle A075500.

Cf. A075911.

Sequence in context: A107395 A036083 A051588 * A000482 A145147 A069379

Adjacent sequences:  A016161 A016162 A016163 * A016165 A016166 A016167

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 6 11:02 EDT 2020. Contains 333273 sequences. (Running on oeis4.)