A190048 Expansion of (8+6*x)/(1-x)^5.

8, 46, 150, 370, 770, 1428, 2436, 3900, 5940, 8690, 12298, 16926, 22750, 29960, 38760, 49368, 62016, 76950, 94430, 114730, 138138, 164956, 195500, 230100, 269100, 312858, 361746, 416150, 476470, 543120, 616528, 697136, 785400, 881790, 986790, 1100898

Offset: 0

Author

Johannes W. Meijer, May 06 2011

Keywords

• nonn
• easy

Comments

Equals the fifth right hand column of A175136.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A175136, A162148, A190049.

Related to A000332 and A091894.

Programs

Magma

[(7*n^4+58*n^3+173*n^2+218*n+96)/12: n in [0..50]]; // Vincenzo Librandi, May 07 2011

Maple

A190048 := proc(n) option remember; a(n):=(7*n^4+58*n^3+173*n^2+218*n+96)/12 end: seq(A190048(n),n=0..35);

Mathematica

LinearRecurrence[{5,-10,10,-5,1}, {8,46,150,370,770}, 30] (* or *) CoefficientList[Series[(8+6*x)/(1-x)^5, {x, 0, 50}], x] (* G. C. Greubel, Jan 10 2018 *)

PARI

x='x+O('x^30); Vec((8+6*x)/(1-x)^5) \\ G. C. Greubel, Jan 10 2018

PARI

for(n=0,50, print1((7*n^4 +58*n^3 +173*n^2 +218*n +96)/12, ", ")) \\ G. C. Greubel, Jan 10 2018

Formula

G.f.: (8+6*x)/(1-x)^5.

a(n) = 8*binomial(n+4,4) + 6*binomial(n+3,4).

a(n) = A091894(4,0)*binomial(n+4,4) + A091894(4,1)*binomial(n+3,4).

a(n) = (7*n^4 +58*n^3 +173*n^2 +218*n +96)/12.