A081041 6th binomial transform of (1,5,0,0,0,0,0,0,...).

1, 11, 96, 756, 5616, 40176, 279936, 1912896, 12877056, 85660416, 564350976, 3688436736, 23944605696, 154551545856, 992612745216, 6347497291776, 40435908673536, 256721001578496, 1624959306694656, 10257555623510016

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 67.

Index entries for linear recurrences with constant coefficients, signature (12,-36).

Formula

a(n) = 12*a(n-1) - 36*a(n-2) for n>1, a(0)=1, a(1)=9.

a(n) = (5*n+6)*6^(n-1).

a(n) = Sum_{k=0..n} (k+1)*5^k*binomial(n, k).

G.f.: (1-x)/(1-6x)^2.

Mathematica

CoefficientList[Series[(1 - x)/(1 - 6 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12, -36}, {1, 11}, 20] (* Harvey P. Dale, Mar 04 2019 *)

Prog

(Magma) [(5*n+6)*6^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Crossrefs

Cf. A081040, A081042.

Sequence in context: A051446 A271632 A055286 * A294724 A115351 A154997

Adjacent sequences: A081038 A081039 A081040 * A081042 A081043 A081044

Keyword

nonn,easy

Author

Paul Barry, Mar 04 2003

Status

approved