A081043 8th binomial transform of (1,7,0,0,0,0,0,...).

1, 15, 176, 1856, 18432, 176128, 1638400, 14942208, 134217728, 1191182336, 10468982784, 91268055040, 790273982464, 6803228196864, 58274116272128, 496979255754752, 4222124650659840, 35747322042253312, 301741175033823232

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (16,-64).

Formula

a(n) = 16*a(n-1) - 64*a(n-2), a(0)=1, a(1)=15.

a(n) = (7n+8)*8^(n-1).

a(n) = Sum_{k=0..n} (k+1)*7^k*binomial(n, k)}.

G.f.: (1-x)/(1-8x)^2.

Mathematica

LinearRecurrence[{16, -64}, {1, 15}, 20] (* or *) Table[(7n+8)8^(n-1), {n, 0, 20}] (* Harvey P. Dale, Feb 22 2012 *)

Prog

(Magma) I:=[1, 15]; [n le 2 select I[n] else 16*Self(n-1)-64*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 23 2012

Crossrefs

Cf. A081042, A081044.

Sequence in context: A024197 A210782 A071535 * A155000 A009146 A012800

Adjacent sequences: A081040 A081041 A081042 * A081044 A081045 A081046

Keyword

easy,nonn

Author

Paul Barry, Mar 04 2003

Status

approved