A014935 a(1)=1, a(n) = n*18^(n-1) + a(n-1).
1, 37, 1009, 24337, 549217, 11886625, 249972193, 5147732449, 104327377633, 2087920281313, 41363059774177, 812583980724961, 15851391939265249, 307372900058661601, 5929573413789876961, 113875823277429211873, 2178347851919531492065, 41524755927216069067489, 789106509357850283000545
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (37,-360,324).
Programs
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PARI
a(n) = (1+18^n*(17*n-1))/289; \\ Jinyuan Wang, Mar 11 2020
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PARI
Vec(-x/((x-1)*(18*x-1)^2) + O(x^20)) \\ Elmo R. Oliveira, May 21 2025
Formula
G.f.: x/((1 - x)*(1 - 18*x)^2). - Stefano Spezia, Mar 11 2020
From Elmo R. Oliveira, May 21 2025: (Start)
E.g.f.: exp(x)*(1 + exp(17*x)*(306*x - 1))/289.
a(n) = (18^n*(17*n - 1) + 1)/289.
a(n) = 36*a(n-1) - 324*a(n-2) + 1 for n > 2.
a(n) = 37*a(n-1) - 360*a(n-2) + 324*a(n-3) for n > 3. (End)
Extensions
More terms from Elmo R. Oliveira, May 21 2025