A170769 Expansion of g.f.: (1+x)/(1-49*x).

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450, 22999326827236998048840050

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 (49).

Crossrefs

Cf. A003945.

Programs

GAP

k:=50;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=50; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=50; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-49*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 50}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

Maxima

A170769(n):=if n=0 then 1 else 50*49^(n-1)$
makelist(A170769(n),n,0,30); /* Martin Ettl, Nov 06 2012 */

PARI

vector(26, n, k=50; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=50; [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)*50^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 50*49^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (50*exp(49*x) - 1)/49. - G. C. Greubel, Oct 11 2019