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 A362718 #6 May 06 2023 05:05:41
%S A362718 1,0,-2,-16,-132,-1216,-12440,-138048,-1601264,-18108928,-161934624,
%T A362718 404007680,92590134208,4221314202624,159324751301248,5730872535686144,
%U A362718 205239818509082880,7450322829180649472,276342876017093172736,10509280308463090102272
%N A362718 Expansion of e.g.f. cos(x)*exp(x^2/2) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.
%F A362718 a(n) = (-1)^n * A001464(2*n).
%F A362718 0 = a(n)*(360*a(n+2) -600*a(n+3) +230*a(n+4) -28*a(n+5) +a(n+6)) +a(n+1)*(216*a(n+2) -296*a(n+3) +84*a(n+4) -6*a(n+5)) +a(n+2)*(66*a(n+2) -56*a(n+3) +15*a(n+4)) -10*a(n+3)^2 for all n >= 0.
%t A362718 a[ n_] := If[ n<0, 0, (2*n)! * SeriesCoefficient[ Cos[x] * Exp[x^2/2], {x, 0, 2*n}]];
%o A362718 (PARI) {a(n) = my(A); if( n<0, 0, A = x*O(x^(2*n)); (2*n)! * polcoef( cos(x + A)*exp(x^2/2 + A), 2*n))};
%o A362718 (SageMath)
%o A362718 def egfExpand(f, step, size) -> list[int]:
%o A362718 x = LazyPowerSeriesRing(QQ, "x").gen()
%o A362718 return [f(x)[step*n] * factorial(step*n) for n in range(size+1)]
%o A362718 def egf(x): return cos(x)*exp(x^2/2)
%o A362718 print(egfExpand(egf, 2, 19)) # _Peter Luschny_, May 02 2023
%Y A362718 Cf. A001464.
%K A362718 sign
%O A362718 0,3
%A A362718 _Michael Somos_, Apr 30 2023