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 A351046 #7 Jan 30 2022 13:14:18
%S A351046 1,4,10,50,200,1250,6850,51850,360100,3211850,26978450,277502750,
%T A351046 2732541700,31870330450,359775334450,4694140275650,59739766446500,
%U A351046 862437753582650,12212993378417650,193324921630774150,3014526392045251300,51925731564631111250,883935015769120470050
%N A351046 a(1)=1; a(2)=4; for n>2, a(n) = a(n-1) + A000217(n)*a(n-2).
%F A351046 E.g.f. A(x) satisfies the differential equation 6*A(x) + (6*x + 2)*A'(x) + (x^2 - 2)*A''(x) = 0, A(0) = 1, A'(0) = 1.
%F A351046 a(n) ~ n! * c * n^(1 + 1/sqrt(2)) / 2^(n/2), where c = 0.42906449224324091038170340685604072807700713285504473...
%t A351046 RecurrenceTable[{a[1]==1, a[2]==4, a[n]==a[n-1] + n*(n+1)/2*a[n-2]}, a, {n, 1, 20}]
%t A351046 nmax = 20; Round[Rest[CoefficientList[Series[(Sqrt[2]*(2 + x^2) - 4*x) * (((2 - x^2)^2 * (1 - 3*Sqrt[2]) * Hypergeometric2F1[2, 3, 3 - 1/Sqrt[2], (2 + Sqrt[2]*x)/4] + 16*(1 + x) * ((Sqrt[2] + x)/(Sqrt[2] - x))^(1/ Sqrt[2]) * ((1 - 3*Sqrt[2]) * Hypergeometric2F1[2, -1/Sqrt[2], 3 - 1/Sqrt[2], -1] + 6*Hypergeometric2F1[3, -1/Sqrt[2], 4 - 1/Sqrt[2], -1])) / (8*(Sqrt[2] - x)^2 * (2 - x^2)^2 * (3*Sqrt[2] * Hypergeometric2F1[3, -1/Sqrt[2], 4 - 1/Sqrt[2], -1] - (6 - Sqrt[2]) * Hypergeometric2F1[2, -1/Sqrt[2], 3 - 1/Sqrt[2], -1]))), {x, 0, nmax}], x]] * Range[nmax]!]
%Y A351046 Cf. A166474.
%K A351046 nonn
%O A351046 1,2
%A A351046 _Vaclav Kotesovec_, Jan 30 2022, following a suggestion from _John M. Campbell_