A056128 a(n) = (9*n + 11)*binomial(n+10, 10)/11.

1, 20, 174, 988, 4277, 15288, 47320, 130832, 330174, 772616, 1696396, 3527160, 6995534, 13312768, 24426552, 43385360, 74847175, 125777340, 206390730, 331405620, 521690715, 806403000, 1225732560, 1834391520, 2706007980, 3938612496, 5661434520, 8043259504

Offset: 0

Author

Barry E. Williams, Jul 08 2000

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A056003.

Programs

GAP

List([0..30], n-> (9*n+11)*Binomial(n+10,10)/11 ); # G. C. Greubel, Jan 18 2020

Magma

[((9*n+11)*Binomial(n+10,10))/11: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014

Maple

seq( (9*n+11)*binomial(n+10, 10)/11, n=0..30); # G. C. Greubel, Jan 18 2020

Mathematica

CoefficientList[Series[(1+8x)/(1-x)^12, {x,0,40}], x] (* Vincenzo Librandi, Jul 30 2014 *)
LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1}, {1,20,174, 988,4277,15288,47320,130832,330174,772616,1696396,3527160}, 40] (* Harvey P. Dale, Jan 14 2015 *)

PARI

vector(31, n, (9*n-2)*binomial(n+9,10)/11 ) \\ G. C. Greubel, Jan 18 2020

Sage

[(9*n+11)*binomial(n+10,10)/11 for n in (0..30)] # G. C. Greubel, Jan 18 2020

Formula

a(n) = (9*n + 11)*binomial(n+10, 10)/11.

G.f.: (1+8*x)/(1-x)^12.

a(n) = 9*binomial(n+11,11) - 8*binomial(n+10,10). - G. C. Greubel, Jan 18 2020

Extensions

New name, from existing formula, added by G. C. Greubel, Jan 18 2020