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A101563
a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+10*x^k).
4
1, 9, 101, 1009, 10001, 99909, 1000001, 10001009, 100000101, 999990009, 10000000001, 100000100909, 1000000000001, 9999999000009, 100000000010101, 1000000010001009, 10000000000000001, 99999999900099909
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * (10)^k * A051731(n+1, k+1).
a(n) = (-1)^n * Sum_{d|n+1} (-10)^(d-1). - G. C. Greubel, Jun 25 2024
MATHEMATICA
A101563[n_]:= (-1)^n*DivisorSum[n+1, (-10)^(#-1) &];
Table[A101563[n], {n, 0, 40}] (* G. C. Greubel, Jun 25 2024 *)
PROG
(Magma)
A101563:= func< n | (&+[(-1)^(n-k)*(10)^k*0^((n+1) mod (k+1)): k in [0..n]]) >;
[A101563(n): n in [0..40]]; // G. C. Greubel, Jun 25 2024
(SageMath)
def A101563(n): return sum((-1)^(n+k)*(10)^k*0^((n+1)%(k+1)) for k in range(n+1))
[A101563(n) for n in range(41)] # G. C. Greubel, Jun 25 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 07 2004
STATUS
approved