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 A001664 M4165 N1732 #28 Jan 13 2025 15:19:08
%S A001664 1,-6,25,-60,-203,3710,-21347,-50400,2465969,-24201342,-14909791,
%T A001664 4154706556,-61829802067,107889525510,13926895008805,-296622934827816,
%U A001664 1387504872714793,80367331405832714,-2381736125794455767,19480923855903871284,721535152036700012069,-29550684521199839783538
%N A001664 Quadratic coefficient of the n-th converging polynomial of Weber functions.
%D A001664 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001664 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001664 P. Wynn, Converging factors for the Weber parabolic cylinder functions of complex argument, <a href="https://doi.org/10.1016/S1385-7258(63)50073-0">part Ia</a>, <a href="https://doi.org/10.1016/S1385-7258(63)50074-2">part Ib</a>, Proc. Konin. Ned. Akad. Weten., Series A, 66 (1963), 721-754 (two parts). In (45) the factor p_{r-2,2} should read p_{r-2,1}.
%H A001664 P. Wynn, <a href="/A001662/a001662_4.pdf">Converging factors for the Weber parabolic cylinder functions ...</a> [Annotated scan of part 2 only]
%p A001664 # equation (47)
%p A001664 prs := proc(r,k)
%p A001664 if r = 0 then
%p A001664 1 ;
%p A001664 elif r = 1 then
%p A001664 -1+k ; # (38)
%p A001664 elif r =2 then
%p A001664 1-3*k+k^2 ;
%p A001664 end if;
%p A001664 end proc:
%p A001664 p := proc(r,s)
%p A001664 option remember ;
%p A001664 local k,a,lambda,mu,phi,theta ;
%p A001664 # theta := 0 ; # valid for Table VII
%p A001664 phi :=1 : # (30) for theta=0
%p A001664 a := 1/2 ; # specific in Table VII
%p A001664 lambda := 2*(a-1) ; # (15)
%p A001664 mu := (a-1/2)*(a-3/2) ; # (13)
%p A001664 if r = s then
%p A001664 return 1; # eq (42)
%p A001664 elif s > r or s <0 then
%p A001664 return 0 ;
%p A001664 elif r <=2 then
%p A001664 coeff(prs(r,k),k,s) ;
%p A001664 elif s = 0 then
%p A001664 # eq (46)
%p A001664 2*(phi+2)*procname(r,1) -8*procname(r,2)
%p A001664 +4*(4*r-lambda-2)*procname(r-1,1)
%p A001664 +2*(lambda*(phi+1)-2*(r-1)*phi-4*r)*procname(r-1,0)
%p A001664 -4*(mu-2*lambda*(r-1)+4*(r-1)^2)*procname(r-2,0) ;
%p A001664 return %/(phi+1) ;
%p A001664 elif s = 1 then
%p A001664 # eq (45)
%p A001664 # note that the 2nd index of the last p is wrong in the publication
%p A001664 4*(phi+2)*procname(r,2) -24*procname(r,3) # unreadable index is 3
%p A001664 +8*(4*r-lambda-2)*procname(r-1,2)
%p A001664 -8*procname(r-1,1)+2*(phi+2)*procname(r-1,0)
%p A001664 +2*(lambda*(phi+1)-2*(r-1)*phi-4*r)*procname(r-1,1)
%p A001664 -4*(lambda-4*r+4)*procname(r-2,0)
%p A001664 -4*(mu-2*lambda*(r-1)+4*(r-1)^2)*procname(r-2,1) ;
%p A001664 return %/(phi+1) ;
%p A001664 elif s= r-1 then
%p A001664 # eq (43)
%p A001664 2*(phi+2)*r*procname(r,r) -8*(r-1)*procname(r-1,r-1)
%p A001664 +2*(phi+2)*procname(r-1,r-2)+2*(lambda*(phi+1)-2*(r-1)*phi-4*r)*procname(r-1,r-1)
%p A001664 -4*procname(r-2,r-3)-4*(lambda-4*r+4)*procname(r-2,r-2) ;
%p A001664 return %/(phi+1) ;
%p A001664 else
%p A001664 # eq (44)
%p A001664 2*(s+1)*(phi+2)*procname(r,s+1) -4*(s+1)*(s+2)*procname(r,s+2)
%p A001664 +4*(4*r-lambda-2)*(s+1)*procname(r-1,s+1)-8*s*procname(r-1,s)
%p A001664 +2*(phi+2)*procname(r-1,s-1)+2*(lambda*(phi+1)-2*(r-1)*phi-4*r)*procname(r-1,s)
%p A001664 -4*procname(r-2,s-2)-4*(lambda-4*r+4)*procname(r-2,s-1)
%p A001664 -4*(mu-2*lambda*(r-1)+4*(r-1)^2)*procname(r-2,s) ;
%p A001664 return %/(phi+1) ;
%p A001664 end if;
%p A001664 end proc:
%p A001664 A001664 := proc(n)
%p A001664 p(n,2) ;
%p A001664 end proc:
%p A001664 seq(A001664(n),n=2..30) ; # _R. J. Mathar_, Jan 13 2025
%Y A001664 Cf. A001663, A001662 (absolute coefficient)
%K A001664 sign
%O A001664 2,2
%A A001664 _N. J. A. Sloane_