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%I #8 Sep 08 2022 08:44:56
%S 1,23,310,3195,27866,216566,1546028,10338515,65635570,399429602,
%T 2346750900,13384232030,74417751940,404759481420,2159510136408,
%U 11327603405955,58528412321250,298354368109930,1502525977613540
%N Convolution of A000108 (Catalan numbers) with A020922.
%C Also convolution of A045505 with A000984 (central binomial coefficients); also convolution of A045492 with A000302 (powers of 4).
%H G. C. Greubel, <a href="/A045530/b045530.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = binomial(n+6, 5)*(A000984(n+6)/A000984(5) - 5*4^(n+1)/(n+6))/2, A000984(n) = binomial(2*n, n).
%F G.f. c(x)/(1-4*x)^(11/2), where c(x) = g.f. for Catalan numbers.
%p seq(coeff(series((sqrt(1-4*x) +4*x-1)/(2*x*(1-4*x)^6), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Jan 13 2020
%t CoefficientList[Series[(Sqrt[1-4*x] +4*x-1)/(2*x*(1-4*x)^6), {x,0,40}], x] (* _G. C. Greubel_, Jan 13 2020 *)
%o (PARI) my(x='x+O('x^40)); Vec( (sqrt(1-4*x) +4*x-1)/(2*x*(1-4*x)^6) ) \\ _G. C. Greubel_, Jan 13 2020
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (Sqrt(1-4*x) +4*x-1)/(2*x*(1-4*x)^6) )); // _G. C. Greubel_, Jan 13 2020
%o (Sage)
%o def A045530_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (sqrt(1-4*x) +4*x-1)/(2*x*(1-4*x)^6) ).list()
%o A045530_list(40) # _G. C. Greubel_, Jan 13 2020
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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