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

0,2

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).

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

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 *)

Prog

(Magma) [((9*n+11)*Binomial(n+10, 10))/11: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014
(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
(GAP) List([0..30], n-> (9*n+11)*Binomial(n+10, 10)/11 ); # G. C. Greubel, Jan 18 2020

Crossrefs

Cf. A056003.

Sequence in context: A010826 A022712 A359718 * A027791 A047819 A163689

Adjacent sequences: A056125 A056126 A056127 * A056129 A056130 A056131

Keyword

easy,nonn

Author

Barry E. Williams, Jul 08 2000

Extensions

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

Status

approved