A081107 7th binomial transform of (1,1,0,0,0,0,...).

1, 8, 63, 490, 3773, 28812, 218491, 1647086, 12353145, 92236816, 686011319, 5084554482, 37569208117, 276825744020, 2034669218547, 14920907602678, 109193914728689, 797590333670424, 5815762849680175, 42338753545671674, 307770170005074861, 2234183456333136028

Offset

0,2

Comments

Main diagonal of array defined by m(0,j) = j; m(i,0) = i and m(i,j) = m(i-1,j) + 6*m(i-1,j-1). - Benoit Cloitre, Jun 13 2003

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-49).

Formula

a(n) = 14*a(n-1) - 49*a(n-2) with n > 1, a(0) = 1, a(1) = 8.

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

G.f.: (1 - 6*x)/(1 - 7*x)^2.

E.g.f.: exp(7*x)*(1 + x). - Stefano Spezia, Mar 05 2023

Mathematica

CoefficientList[Series[(1 - 6 x)/(1 - 7 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

Prog

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

Crossrefs

Cf. A081106, A081108, A006234.

Sequence in context: A085433 A171313 A370038 * A164592 A242631 A001090

Adjacent sequences: A081104 A081105 A081106 * A081108 A081109 A081110

Keyword

nonn,easy

Author

Paul Barry, Mar 07 2003

Status

approved