A014936 a(1)=1, a(n) = n*19^(n-1) + a(n-1).
1, 39, 1122, 28558, 680163, 15536757, 344857924, 7495831836, 160347899205, 3387224876995, 70828953712806, 1468712060491434, 30241806008351527, 618983574479950353, 12604083861223212168, 255502116339219984952, 5159006146988779835529, 103805969587115219182431
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (39,-399,361).
Programs
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Mathematica
RecurrenceTable[{a[1]==1,a[n]==n*19^(n-1)+a[n-1]},a,{n,20}] (* Harvey P. Dale, Oct 01 2012 *) -
PARI
a(n) = (1+19^n*(18*n-1))/324; \\ Jinyuan Wang, Mar 11 2020
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PARI
my(x='x+O('x^19)); Vec(-x/((x-1)*(19*x-1)^2)) \\ Elmo R. Oliveira, May 22 2025
Formula
G.f.: x/((1 - x)*(1 - 19*x)^2). - Stefano Spezia, Mar 11 2020
From Elmo R. Oliveira, May 22 2025: (Start)
E.g.f.: exp(x)*(1 + exp(18*x)*(342*x - 1))/324.
a(n) = (19^n*(18*n - 1) + 1)/324.
a(n) = 38*a(n-1) - 361*a(n-2) + 1 for n > 2.
a(n) = 39*a(n-1) - 399*a(n-2) + 361*a(n-3) for n >= 4. (End)
Extensions
More terms from Elmo R. Oliveira, May 22 2025