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A190049
Expansion of (16+24*x+2*x^2)/(x-1)^6.
4
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
0,1
COMMENTS
Equals the sixth right hand column of A175136.
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.
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 *)
PROG
(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
(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
CROSSREFS
Related to A000389 and A091894.
Sequence in context: A316286 A306050 A248621 * A317227 A138571 A047641
KEYWORD
nonn,easy
AUTHOR
Johannes W. Meijer, May 06 2011
STATUS
approved