A190051 Expansion of (1-x)*(10*x^4-20*x^3+16*x^2-6*x+1)/(1-2*x)^5.

1, 3, 12, 44, 150, 482, 1476, 4344, 12368, 34240, 92544, 244992, 636928, 1629696, 4111360, 10242048, 25227264, 61505536, 148570112, 355860480, 845807616, 1996095488, 4680056832, 10906763264, 25275924480, 58271465472

Offset: 0

Author

Johannes W. Meijer, May 06 2011

Keywords

• nonn
• easy

Comments

The third left hand column of triangle A175136.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..300 from Vincenzo Librandi)
• Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Crossrefs

Cf. A175136, A011782, A190050.

Related to A003472.

Programs

Magma

[1] cat [(264 + 214*n + 14*n^3 + 83*n^2 + n^4)*2^(n-7)/3: n in [1..30]]; // G. C. Greubel, Jan 10 2018

Maple

A190051:= proc(n) option remember; if n=0 then A190051(n):=1 else A190051(n):= (264+214*n+14*n^3+83*n^2+n^4)*2^(n-7)/3 fi: end: seq (A190051(n), n=0..25);

Mathematica

Join[{1}, LinearRecurrence[{10,-40,80,-80,32}, {3,12,44,150,482}, 30]] (* or *) CoefficientList[Series[(1 - x)*(10*x^4 -20*x^3 +16*x^2 -6*x + 1)/(1 -2*x)^5, {x, 0, 50}], x] (* G. C. Greubel, Jan 10 2018 *)

PARI

x='x+O('x^30); Vec((1-x)*(10*x^4-20*x^3+16*x^2-6*x+1)/(1-2*x)^5) \\ G. C. Greubel, Jan 10 2018

PARI

for(n=0,30, print1(if(n==0,1,(264 + 214*n + 14*n^3 + 83*n^2 + n^4)*2^(n-7)/3), ", ")) \\ G. C. Greubel, Jan 10 2018

Formula

G.f.: (1-x)*(10*x^4-20*x^3+16*x^2-6*x+1)/(1-2*x)^5.

a(n) = (264 + 214*n + 14*n^3 + 83*n^2 + n^4)*2^(n-7)/3 for n >=1 with a(0)=1.

a(n-4) = A003472(n) -7*A003472(n-1) +22*A003472(n-2) -36*A003472(n-3) +30*A003472(n-4) -10*A003472(n-5) for n>=5 with a(0) = 1.