A081106 6th binomial transform of (1,1,0,0,0,0,...).

1, 7, 48, 324, 2160, 14256, 93312, 606528, 3919104, 25194240, 161243136, 1027924992, 6530347008, 41358864384, 261213880320, 1645647446016, 10344069660672, 64885527871488, 406239826673664, 2538998916710400, 15843353240272896, 98716277881700352, 614234617930579968

Offset

0,2

Comments

Main diagonal of array defined by m(1,j) = j; m(i,1) = i and m(i,j) = m(i-1,j) + 5*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 (12,-36).

Formula

a(n) = 12*a(n-1) - 36*a(n-2) with n > 1, a(0) = 1, a(1) = 7.

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

G.f.: (1 - 5*x)/(1 - 6*x)^2.

E.g.f.: exp(6*x)*(1 + x). - Stefano Spezia, Mar 05 2023

Mathematica

CoefficientList[Series[(1 - 5 x)/(1 - 6 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12, -36}, {1, 7}, 30] (* Harvey P. Dale, Nov 07 2013 *)

Prog

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

Crossrefs

Cf. A079028, A081105, A006234.

Sequence in context: A171312 A186161 A370037 * A289785 A036829 A164591

Adjacent sequences: A081103 A081104 A081105 * A081107 A081108 A081109

Keyword

nonn,easy

Author

Paul Barry, Mar 07 2003

Status

approved