A170744 Expansion of g.f.: (1+x)/(1-24*x).

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400, 12621432073901152665600, 302914369773627663974400

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..724
• Index entries for linear recurrences with constant coefficients, signature (24).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

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

Magma

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

Maple

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

Mathematica

Join[{1},NestList[24#&,25,30]] (* Harvey P. Dale, Jan 19 2019 *)

PARI

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

Python

for i in range(31):print(i,25*24**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

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

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*25^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 25*24^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (25*exp(24*x) - 1)/24. - G. C. Greubel, Sep 25 2019