This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A026933 #44 Feb 19 2025 12:20:01
%S A026933 1,2,11,52,269,1414,7575,41064,224665,1237898,6859555,38187164,
%T A026933 213408805,1196524814,6727323439,37915058384,214140178225,
%U A026933 1211694546194,6867622511675,38981807403268,221562006394173,1260814207833750,7182599953332423,40958645048598840,233779564099963081
%N A026933 Self-convolution of array T given by A008288.
%H A026933 Vincenzo Librandi, <a href="/A026933/b026933.txt">Table of n, a(n) for n = 0..200</a>
%H A026933 Paul Barry, <a href="https://doi.org/10.3390/math13020242">Extensions of Riordan Arrays and Their Applications</a>, Mathematics (2025) Vol. 13, No. 2, 242. See p. 15.
%F A026933 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
%F A026933 G.f.: 1/((1+x)*sqrt(1-6*x+x^2)). - _Vladeta Jovovic_, May 13 2003
%F A026933 a(n) = (-1)^n*Sum_{k=0...n} (-1)^k*A001850(k). - _Benoit Cloitre_, Sep 28 2005
%F A026933 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
%F A026933 Self-convolution yields A204062; self-convolution of A204061. - _Paul D. Hanna_, Jan 10 2012
%F A026933 From _Vaclav Kotesovec_, Oct 08 2012: (Start)
%F A026933 Recurrence: n*a(n) = (5*n-3)*a(n-1) + (5*n-2)*a(n-2) - (n-1)*a(n-3).
%F A026933 a(n) ~ sqrt(24+17*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi*n)). (End)
%F A026933 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
%t A026933 Table[SeriesCoefficient[1/(1+x)/Sqrt[1-6*x+x^2],{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 08 2012 *)
%t A026933 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 *)
%t A026933 A026933[n_]:= Sum[(Binomial[n, k]*Hypergeometric2F1[-k,k-n,-n,-1])^2, {k,0,n}];
%t A026933 Table[A026933[n], {n, 0, 40}] (* _G. C. Greubel_, May 25 2021 *)
%o A026933 (PARI) /* Sum of squares of Delannoy numbers: */
%o A026933 {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
%o A026933 (PARI) /* Involving squares of companion Pell numbers: */
%o A026933 {A002203(n)=polcoeff(2*x*(1+x)/(1-2*x-x^2+x*O(x^n)),n)}
%o A026933 {a(n)=polcoeff(exp(sum(k=1, n, A002203(k)^2/2*x^k/k)+x*O(x^n)), n)}
%o A026933 \\ _Paul D. Hanna_, Jan 10 2012
%o A026933 (PARI) my(x='x+O('x^66)); Vec( 1/(1+x)/sqrt(1-6*x+x^2) ) \\ _Joerg Arndt_, May 04 2013
%o A026933 (Sage)
%o A026933 def A026933_list(prec):
%o A026933 P.<x> = PowerSeriesRing(ZZ, prec)
%o A026933 return P( 1/((1+x)*sqrt(1-6*x+x^2)) ).list()
%o A026933 A026933_list(40) # _G. C. Greubel_, May 25 2021
%Y A026933 Cf. A002203, A008288, A204061, A204062.
%K A026933 nonn
%O A026933 0,2
%A A026933 _Clark Kimberling_
%E A026933 More terms from _Vladeta Jovovic_, May 13 2003