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A118195
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Self-convolution square-root of A118191, where A118191 is column 0 of the matrix square of triangle A118190 with A118190(n,k) = (5^k)^(n-k).
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1
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1, 1, 3, 23, 411, 15771, 1353045, 252512065, 106798723795, 99080638950595, 208993838938550873, 968425792397232696773, 10208662119796586878979989, 236472963735267887311598074949, 12462692176683507314938059670486683
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| In general, sqrt( Sum_{n>=0} x^n/(1 - q^n*x) ) is an integer series whenever q == 1 (mod 4).
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FORMULA
| G.f.: A(x) = sqrt( Sum_{n>=0} x^n/(1-5^n*x) ).
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EXAMPLE
| A(x) = 1 + x + 3*x^2 + 23*x^3 + 411*x^4 + 15771*x^5 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 52*x^3 + 877*x^4 + 32502*x^5 +...
= 1/(1-x) + x/(1-5x) + x^2/(1-25x) + x^3/(1-125x) +...
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PROG
| (PARI) a(n)=polcoeff(sqrt(sum(k=0, n, sum(j=0, k, (5^j)^(k-j) )*x^k+x*O(x^n))), n)
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CROSSREFS
| Cf. A118190.
Sequence in context: A068338 A114601 A178315 * A055326 A133338 A116986
Adjacent sequences: A118192 A118193 A118194 * A118196 A118197 A118198
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2006
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