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 A002695 M4642 N1985 #46 Sep 28 2024 07:36:30
%S A002695 1,9,66,450,2955,18963,119812,748548,4637205,28537245,174683718,
%T A002695 1064611782,6464582943,39132819495,236256182280,1423046656008,
%U A002695 8554078990377,51327262010673,307488810131530,1839455028693450
%N A002695 P_n'(3), where P_n is n-th Legendre polynomial.
%D A002695 H. Bateman, Some problems in potential theory, Messenger Math., 52 (1922), 71-78.
%D A002695 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002695 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002695 T. D. Noe, <a href="/A002695/b002695.txt">Table of n, a(n) for n=1..100</a>
%H A002695 H. Bateman, <a href="/A002692/a002692.pdf">Some problems in potential theory</a>, Messenger Math., 52 (1922), 71-78. [Annotated scanned copy]
%H A002695 John Riordan, <a href="/A002720/a002720_3.pdf">Letter to N. J. A. Sloane, Sep 26 1980 with notes on the 1973 Handbook of Integer Sequences</a>. Note that the sequences are identified by their N-numbers, not their A-numbers.
%F A002695 G.f.: x*(1-6*x+x^2)^(-3/2). [corrected by _Vaclav Kotesovec_, Oct 04 2012]
%F A002695 a(n) = Gegenbauer_C(n,3/2,3). - _Paul Barry_, Apr 20 2009
%F A002695 D-finite with recurrence: -n*a(n-2) + 3*(2*n-1)*a(n-1) + (1-n)*a(n) = 0. - _Vaclav Kotesovec_, Oct 04 2012
%F A002695 a(n) ~ (3+2*sqrt(2))^n*sqrt(n)/(4*sqrt(2*Pi)*sqrt(3*sqrt(2)-4)). - _Vaclav Kotesovec_, Oct 04 2012
%F A002695 a(n) = (n+1) * n * A001003(n)/2, n>0. - _Vladimir Kruchinin_, Mar 29 2013
%F A002695 a(n) = Sum_{i=1..n} i*binomial(n+i,i)*binomial(n,i)/2. - _Gerry Martens_, Apr 08 2018
%t A002695 Table[SeriesCoefficient[x*(1-6x+x^2)^(-3/2),{x,0,n}],{n,1,20}] (* _Vaclav Kotesovec_, Oct 04 2012 *)
%t A002695 a[n_]:= Sum[(i Binomial[n+i+1,i] Binomial[n+1,i]),{i,1,n+1}]/2
%t A002695 Table[a[n], {n, 0, 20}] (* _Gerry Martens_, Apr 08 2018 *)
%o A002695 (PARI)
%o A002695 N = 66; x = 'x + O('x^N);
%o A002695 gf = x*(1-6*x+x^2)^(-3/2);
%o A002695 Vec(gf)
%o A002695 /* _Joerg Arndt_, Mar 29 2013 */
%Y A002695 Cf. A001850.
%K A002695 nonn,easy
%O A002695 1,2
%A A002695 _N. J. A. Sloane_, _Simon Plouffe_