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A026933 a(n) = self-convolution of array T given by A008288. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

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]

From Vaclav Kotesovec, Oct 08 2012: (Start)

Recurrence: n*a(n) = (5*n-3)*a(n-1) + (5*n-2)*a(n-2) - (n-1)*a(n-3).

a(n) ~ sqrt(24+17*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi*n)). (End)

0 = +a(n)*(+a(n+1) -8*a(n+2) -7*a(n+3) +2*a(n+4)) +a(n+1)*(-2*a(n+1) +22*a(n+2) +20*a(n+3) -7*a(n+4)) +a(n+2)*(+30*a(n+2) +22*a(n+3) -8*a(n+4)) +a(n+3)*(-2*a(n+3) +a(n+4)) for all n in Z. - Michael Somos, Jun 27 2017

MATHEMATICA

Table[SeriesCoefficient[1/(1+x)/Sqrt[1-6*x+x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2012 *)

a[ n_] := Sum[ SeriesCoefficient[ SeriesCoefficient[ 1 / (1 - x - y - x y) , {x, 0, n - k}] , {y, 0, k}]^2, {k, 0, n}]; (* Michael Somos, Jun 27 2017 *)

PROG

(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

CROSSREFS

Cf. A008288, A204061, A204062, A002203.

Sequence in context: A026996 A110308 A027201 * A052171 A168022 A030281

Adjacent sequences:  A026930 A026931 A026932 * A026934 A026935 A026936

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Vladeta Jovovic, May 13 2003

STATUS

approved

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Last modified February 20 18:39 EST 2018. Contains 299381 sequences. (Running on oeis4.)