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Search: id:A118191
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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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+0
4
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| 1, 2, 7, 52, 877, 32502, 2740627, 507843752, 214111484377, 198376465625002, 418186492923828127, 1937270172119160156252, 20419262349796295263671877, 472966350615029335022460937502, 24925857360591180741786959228515627
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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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/(1-5x) + x^2/(1-25x) + x^3/(1-125x) + ...
= 1 + 2*x + 7*x^2 + 52*x^3 + 877*x^4 + 32502*x^5 + ...
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PROGRAM
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(PARI) a(n)=sum(k=0, n, (5^k)^(n-k))
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CROSSREFS
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Cf. A118190 (triangle), A118195 (A(x)^(1/2)), A118192 (antidiagonal sums).
Sequence in context: A086902 A138737 A046662 this_sequence A005588 A106898 A106899
Adjacent sequences: A118188 A118189 A118190 this_sequence A118192 A118193 A118194
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2006
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