A067412 Fourth column of triangle A067410.

1, 5, 40, 320, 2560, 20480, 163840, 1310720, 10485760, 83886080, 671088640, 5368709120, 42949672960, 343597383680, 2748779069440, 21990232555520, 175921860444160, 1407374883553280, 11258999068426240

Offset: 0

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy

Comments

The fifth column gives [1,6,60,600,6000,60000,...].

a(n+1) = A157176(A016957(n)). [From Reinhard Zumkeller, Feb 24 2009]

Links

• Index entries for linear recurrences with constant coefficients, signature (8).

Crossrefs

Cf. A067411 (third column), A067413 (sixth column), A001018 (powers of 8).

Programs

Mathematica

Join[{1},NestList[8#&,5,20]] (* or *) CoefficientList[Series[ (1-3x)/ (1-8x),{x,0,20}],x] (* Harvey P. Dale, May 14 2011 *)

Formula

a(n)= A067410(n+3, 3). a(n)= 5*8^(n-1), n>=1, a(0)=1.

G.f.: (1-3*x)/(1-8*x).

E.g.f.: (5*exp(8*x)+3)/8 = exp(4*x)*(cosh(4*x)+sinh(4*x)/4) - Paul Barry, Nov 20 2003