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 A045622 #8 Sep 08 2022 08:44:56
%S A045622 1,25,362,3973,36646,299530,2238676,15613741,103054094,650194974,
%T A045622 3950996556,23257207714,133217073276,745218012084,4083224828328,
%U A045622 21966983072637,116268166691358,606474982072982,3122157367765788
%N A045622 Convolution of A000108 (Catalan numbers) with A045543.
%C A045622 Also convolution of A045530 with A000984 (central binomial coefficients); also convolution of A045505 with A000302 (powers of 4).
%H A045622 G. C. Greubel, <a href="/A045622/b045622.txt">Table of n, a(n) for n = 1..1000</a>
%F A045622 a(n) = binomial(n+6, 5)*(4^(n+1) - A000984(n+6)/A000984(5))/2, A000984(n) = binomial(2*n, n).
%F A045622 G.f.: x*c(x)/(1-4*x)^6, where c(x) = g.f. for Catalan numbers.
%p A045622 seq(coeff(series((1-sqrt(1-4*x))/(2*(1-4*x)^6), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Jan 13 2020
%t A045622 CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x*(1-4*x)^6), {n,0,40}], x] (* _G. C. Greubel_, Jan 13 2020 *)
%o A045622 (PARI) my(x='x+O('x^40)); Vec((1-sqrt(1-4*x))/(2*(1-4*x)^6)) \\ _G. C. Greubel_, Jan 13 2020
%o A045622 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))/(2*(1-4*x)^6) )); // _G. C. Greubel_, Jan 13 2020
%o A045622 (Sage)
%o A045622 def A045622_list(prec):
%o A045622 P.<x> = PowerSeriesRing(ZZ, prec)
%o A045622 return P( (1-sqrt(1-4*x))/(2*(1-4*x)^6) ).list()
%o A045622 A045622_list(40) # _G. C. Greubel_, Jan 13 2020
%K A045622 easy,nonn
%O A045622 1,2
%A A045622 _Wolfdieter Lang_