A081042 7th binomial transform of (1,6,0,0,0,0,0,0,...).

1, 13, 133, 1225, 10633, 88837, 722701, 5764801, 45294865, 351652861, 2703691669, 20620693177, 156208812697, 1176509412085, 8816899947037, 65787638066353, 488998835524129, 3622389432086509, 26752509108528805, 197038045347164329

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 (14,-49).

Formula

a(n) = 14*a(n-1) - 49*a(n-2) for n>1, a(0)=1, a(1)=13.

a(n) = (6*n+7)*7^(n-1).

a(n) = Sum_{k=0..n} (k+1)*6^k*binomial(n, k).

G.f.: (1-x)/(1-7*x)^2.

Mathematica

CoefficientList[Series[(1 - x)/(1 - 7 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{14, -49}, {1, 13}, 20] (* Harvey P. Dale, Jan 24 2014 *)

Prog

(Magma) [(6*n+7)*7^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Crossrefs

Cf. A081041, A081042.

Sequence in context: A199144 A198664 A332243 * A329019 A016153 A187732

Adjacent sequences: A081039 A081040 A081041 * A081043 A081044 A081045

Keyword

nonn,easy

Author

Paul Barry, Mar 04 2003

Status

approved