A052245 Expansion of 10*x / ((1 - x) * (1 - 10*x)^2) in powers of x.

0, 10, 210, 3210, 43210, 543210, 6543210, 76543210, 876543210, 9876543210, 109876543210, 1209876543210, 13209876543210, 143209876543210, 1543209876543210, 16543209876543210, 176543209876543210, 1876543209876543210, 19876543209876543210, 209876543209876543210

Offset: 0

Author

Henry Bottomley, Feb 01 2000

Keywords

• easy
• nonn

Comments

This is not the same as A052246. They differ at a(11) and beyond. - Michael Somos, Sep 14 2014

Links

• Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Crossrefs

Cf. A014925, A052246.

Programs

Maple

seq(sum(x*10^x,x=0..a),a=0..100); # Jorge Coveiro, Dec 22 2004
a:=n->sum((10^(n-j)*(n-j)),j=0..n): seq(a(n), n=0..16); # Zerinvary Lajos, Jun 05 2008

PARI

concat(0, Vec(-10*x/((x-1)*(10*x-1)^2) + O(x^100))) \\ Colin Barker, Sep 13 2014

Formula

a(n) = n*10^n+a(n-1), a(0) = 0; a(n) = ((9n-1)*10^n + 1) * 10 / 81; a(n) = A014925(n)*10.

a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, Sep 13 2014

G.f.: -10*x / ((x-1)*(10*x-1)^2). - Colin Barker, Sep 13 2014

Extensions

More terms from Colin Barker, Sep 13 2014