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A118191
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Row sums of triangle A118190: a(n) = Sum_{k=0..n} 5^(k*(n-k)) for n>=0.
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4
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1, 2, 7, 52, 877, 32502, 2740627, 507843752, 214111484377, 198376465625002, 418186492923828127, 1937270172119160156252, 20419262349796295263671877, 472966350615029335022460937502, 24925857360591180741786959228515627
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OFFSET
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0,2
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COMMENTS
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Self-convolution of A118195; in general, sqrt(Sum_{n>=0} x^n/(1-q^n*x)) is an integer series whenever q == 1 (mod 4). Also equals column 0 of the matrix square of triangle A118190, where [A118190^2](n,k) = a(n-k)*5^(k*(n-k)) for n>=k>=0.
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LINKS
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FORMULA
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G.f.: A(x) = Sum_{n>=0} x^n/(1-5^n*x).
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EXAMPLE
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A(x) = 1/(1-x) + x/(1-5*x) + x^2/(1-25*x) + x^3/(1-125*x) + ...
= 1 + 2*x + 7*x^2 + 52*x^3 + 877*x^4 + 32502*x^5 + ...
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MATHEMATICA
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Table[Sum[5^(k*(n-k)), {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Jun 29 2021 *)
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PROG
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(PARI) a(n)=sum(k=0, n, (5^k)^(n-k))
(Magma) [(&+[5^(k*(n-k)): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jun 29 2021
(Sage) [sum(5^(k*(n-k)) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 29 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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