A108487 Sum binomial(2n-2k,2k)10^(n-k), k=0..floor(n/2).

1, 10, 110, 1600, 25100, 395000, 6201000, 97280000, 1526010000, 23938500000, 375525100000, 5890896000000, 92411011000000, 1449659710000000, 22740940010000000, 356739136000000000, 5596198360100000000

Offset: 0

Author

Paul Barry, Jun 04 2005

Keywords

• easy
• nonn

Comments

In general, sum{k=0..floor(n/2), C(2n-2k,2k)a^k*b^(n-k)} has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-80,200,-100).

Programs

Mathematica

Table[Sum[Binomial[2n-2k,2k]10^(n-k),{k,0,Floor[n/2]}],{n,0,30}] (* or *) LinearRecurrence[{20,-80,200,-100},{1,10,110,1600},30] (* Harvey P. Dale, Mar 20 2023 *)

Formula

G.f.: (1-10x-10x^2)/(1-20x-80x^2-200x^3+100x^4); a(n)=20a(n-1)+80a(n-2)+200a(n-3)-100a(n-4).