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

Author

Paul Barry, Mar 07 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A079028, A081105, A006234.

Programs

Magma

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

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 *)

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