A014938 a(1)=1, a(n) = n*21^(n-1) + a(n-1).

1, 43, 1366, 38410, 1010815, 25515421, 625878268, 15034586596, 355440320845, 8298240786655, 191776931546866, 4395106938053518, 100020864586079851, 2262634152933752305, 50921433140756382520, 1140878530467983299336, 25460546264581733880793, 566215511176052187986131

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (43,-483,441).

Programs

Mathematica

A014938[n_] := (21^n*(20*n - 1) + 1)/400; Array[A014938, 25] (* or *)
LinearRecurrence[{43, -483, 441}, {1, 43, 1366}, 25] (* Paolo Xausa, May 29 2025 *)

PARI

a(n) = (1+21^n*(20*n-1))/400; \\ Jinyuan Wang, Mar 11 2020

PARI

my(x='x+O('x^19)); Vec(-x/((x-1)*(21*x-1)^2)) \\ Elmo R. Oliveira, May 22 2025

Formula

G.f.: x/((1 - x)*(1 - 21*x)^2). - Stefano Spezia, Mar 11 2020

From Elmo R. Oliveira, May 22 2025: (Start)

E.g.f.: exp(x)*(1 + exp(20*x)*(420*x - 1))/400.

a(n) = (21^n*(20*n - 1) + 1)/400.

a(n) = 42*a(n-1) - 441*a(n-2) + 1 for n > 2.

a(n) = 43*a(n-1) - 483*a(n-2) + 441*a(n-3) for n >= 4. (End)

Extensions

More terms from Elmo R. Oliveira, May 22 2025