A014943 a(1)=1, a(n) = n*25^(n-1) + a(n-1).

1, 51, 1926, 64426, 2017551, 60611301, 1769595676, 50597720676, 1423888736301, 39570861392551, 1088612609439426, 29698842101626926, 804559224181705051, 21666184895568423801, 580459729664855533176, 15481620923512511783176, 411293715135090880923801, 10888672679559224181705051

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (51,-675,625).

Programs

Mathematica

RecurrenceTable[{a[1]==1,a[n]==n*25^(n-1)+a[n-1]},a,{n,20}] (* or *)
LinearRecurrence[{51,-675,625},{1,51,1926},20] (* Harvey P. Dale, Dec 16 2012 *)

PARI

Vec(x/((1-x)*(1-25*x)^2) + O(x^19)) \\ Elmo R. Oliveira, May 18 2025

Formula

a(n) = 51*a(n-1) - 675*a(n-2) + 625*a(n-3), a(1)=1, a(2)=51, a(3)=1926. - Harvey P. Dale, Dec 16 2012

From Elmo R. Oliveira, May 18 2025: (Start)

G.f.: -x/((x-1)*(25*x-1)^2).

E.g.f.: exp(x)*(1 + exp(24*x)*(600*x - 1))/576.

a(n) = (26^n*(25*n - 1) + 1)/576.

a(n) = 50*a(n-1) - 625*a(n-2) + 1 for n > 2. (End)

Extensions

More terms from Elmo R. Oliveira, May 18 2025