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A026933
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a(n) = self-convolution of array T given by A008288.
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5
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1, 2, 11, 52, 269, 1414, 7575, 41064, 224665, 1237898, 6859555, 38187164, 213408805, 1196524814, 6727323439, 37915058384, 214140178225, 1211694546194, 6867622511675, 38981807403268, 221562006394173, 1260814207833750, 7182599953332423, 40958645048598840, 233779564099963081
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) = Sum_{k=0..n} D(n-k,k)^2 where D(n,k) = A008288(n,k) are the Delannoy numbers. [Paul D. Hanna, Jan 10 2012]
G.f.: 1/(1+x)/sqrt(1-6*x+x^2). - Vladeta Jovovic, May 13 2003
a(n)=(-1)^n*sum_{k=0...n}(-1)^k*A001850(k) - Benoit Cloitre, Sep 28 2005
G.f.: exp( Sum_{n>=1} A002203(n)^2/2 * x^n/n ) where A002203 are the companion Pell numbers. [Paul D. Hanna, Jan 10 2012]
Self-convolution yields A204062; self-convolution of A204061. [Paul D. Hanna, Jan 10 2012]
Recurrence: n*a(n) = (5*n-3)*a(n-1) + (5*n-2)*a(n-2) - (n-1)*a(n-3). - Vaclav Kotesovec, Oct 08 2012
a(n) ~ sqrt(24+17*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 08 2012
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MATHEMATICA
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Table[SeriesCoefficient[1/(1+x)/Sqrt[1-6*x+x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2012 *)
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PROG
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(PARI) /* Sum of squares of Delannoy numbers: */
{a(n)=sum(k=0, n, polcoeff(polcoeff(1/(1-x-y-x*y +x*O(x^n)+y*O(y^k)), n-k, x), k, y)^2)} \\ Paul D. Hanna, Jan 10 2012
(PARI) /* Involving squares of companion Pell numbers: */
{A002203(n)=polcoeff(2*x*(1+x)/(1-2*x-x^2+x*O(x^n)), n)}
{a(n)=polcoeff(exp(sum(k=1, n, A002203(k)^2/2*x^k/k)+x*O(x^n)), n)}
\\ Paul D. Hanna, Jan 10 2012
(PARI) x='x+O('x^66); Vec( 1/(1+x)/sqrt(1-6*x+x^2) ) \\ Joerg Arndt, May 04 2013
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CROSSREFS
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Cf. A008288, A204061, A204062, A002203.
Sequence in context: A026996 A110308 A027201 * A052171 A168022 A030281
Adjacent sequences: A026930 A026931 A026932 * A026934 A026935 A026936
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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More terms from Vladeta Jovovic, May 13 2003
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STATUS
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approved
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