A170745 Expansion of g.f.: (1+x)/(1-25*x).

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156250, 38743019104003906250, 968575477600097656250, 24214386940002441406250, 605359673500061035156250

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..715
• Index entries for linear recurrences with constant coefficients, signature (25).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=26;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Magma

k:=26; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

Maple

k:=26; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+x)/(1-25*x),{x,0,20}],x] (* or *) Join[ {1}, NestList[25#&,26,20]] (* Harvey P. Dale, Aug 08 2019 *)

PARI

vector(26, n, k=26; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,26*25**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=26; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*26^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 26*25^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (26*exp(25*x) - 1)/25. - G. C. Greubel, Sep 25 2019