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 A228192 #8 Apr 02 2025 15:17:03
%S A228192 1,3,321,1462563,252055236609,1569245074591690083,
%T A228192 345299757825442889707393857,2653337188651000290233505189314055363,
%U A228192 706829476163540077094231781323762631545566527489,6496844758902641761809431955916116052361210081093847336070467
%N A228192 a(n) = A001850(n^2), where A001850 forms the central Delannoy numbers.
%F A228192 a(n) = Sum_{k=0..n^2} binomial(n^2, k) * binomial(n^2+k, k).
%F A228192 a(n) = [x^(n^2)] 1/sqrt(1 - 6*x + x^2).
%F A228192 Equals the logarithmic derivative of A228193, after ignoring the initial term.
%e A228192 L.g.f.: L(x) = 3*x + 321*x^2/2 + 1462563*x^3/3 + 252055236609*x^4/4 +...
%e A228192 where exponentiation yields the g.f. of A228193:
%e A228192 exp(L(x)) = 1 + 3*x + 165*x^2 + 488007*x^3 + 63015285321*x^4 + 313849204040245803*x^5 +...+ A228193(n)*X^n +...
%o A228192 (PARI) {a(n)=sum(k=0,n^2,binomial(n^2,k)*binomial(n^2+k,k))}
%o A228192 for(n=0,20,print1(a(n),", "))
%o A228192 (PARI) {A001850(n)=polcoeff(1/sqrt(1 - 6*x + x^2 + x*O(x^n)), n)}
%o A228192 {a(n)=A001850(n^2)}
%o A228192 for(n=0,20,print1(a(n),", "))
%Y A228192 Cf. A228193, A001850.
%K A228192 nonn
%O A228192 0,2
%A A228192 _Paul D. Hanna_, Aug 15 2013