A170768 Expansion of g.f.: (1+x)/(1-48*x).

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192, 16887812686401712963977216

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries for linear recurrences with constant coefficients, signature (48).

Crossrefs

Cf. A003945.

Programs

GAP

k:=49;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=49; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=49; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-48*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 49}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

PARI

vector(26, n, k=49; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=49; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*49^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 49*48^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (49*exp(48*x) - 1)/48. - G. C. Greubel, Oct 11 2019