A190049 Expansion of (16+24*x+2*x^2)/(x-1)^6.

16, 120, 482, 1412, 3402, 7168, 13692, 24264, 40524, 64504, 98670, 145964, 209846, 294336, 404056, 544272, 720936, 940728, 1211098, 1540308, 1937474, 2412608, 2976660, 3641560, 4420260, 5326776, 6376230, 7584892

Offset: 0

Author

Johannes W. Meijer, May 06 2011

Keywords

• nonn
• easy

Comments

Equals the sixth 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 (6,-15,20,-15,6,-1).

Crossrefs

Cf. A175136, A162148, A190048.

Related to A000389 and A091894.

Programs

Magma

[(21*n^5+245*n^4+1105*n^3+2395*n^2+2474*n+960)/60: n in [0..50]]; // Vincenzo Librandi, May 07 2011

Maple

A190049 := proc(n) option remember; a(n):=(21*n^5 +245*n^4 +1105*n^3 +2395*n^2 +2474*n +960)/60 end: seq(A190049(n),n=0..27);

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1}, {16,120,482,1412,3402,7168}, 30] (* or *) CoefficientList[Series[(16 +24*x +2*x^2)/(1-x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jan 10 2018 *)

PARI

x='x+O('x^30); Vec((16 +24*x +2*x^2)/(1-x)^6) \\ G. C. Greubel, Jan 10 2018

PARI

for(n=0,30, print1((21*n^5 +245*n^4 +1105*n^3 +2395*n^2 +2474*n +960)/60, ", ")) \\ G. C. Greubel, Jan 10 2018

Formula

G.f.: (16 +24*x +2*x^2)/(1-x)^6.

a(n) = 16*binomial(n+5,5) +24*binomial(n+4,5) +2*binomial(n+3,5).

a(n) = A091894(5,0)*binomial(n+5,5) + A091894(5,1)*binomial(n+4,5) + A091894(5,2)*binomial(n+3,5).

a(n) = (21*n^5 +245*n^4 +1105*n^3 +2395*n^2 +2474*n +960)/60.