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A100328 Column 1 of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324, with leading zero omitted. 2

%I

%S 1,4,20,116,736,4952,34716,250868,1855520,13979192,106901032,

%T 827644424,6474611984,51100656544,406400018092,3253636464756,

%U 26201323746880,212093247874904,1724793778005528,14084738953391768,115447965121881856

%N Column 1 of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324, with leading zero omitted.

%C Self-convolution of A100327, which equals the row sums of triangle A100326.

%H Vaclav Kotesovec, <a href="/A100328/b100328.txt">Table of n, a(n) for n = 0..650</a>

%F G.f. A(x) = (1+G003169(x))*G003169(x)/x, where G003169(x) is the g.f. of A003169.

%F Recurrence: 4*(n+1)*(2*n+1)*(17*n^2 - 28*n + 12)*a(n) = (1207*n^4 - 1988*n^3 + 1013*n^2 - 124*n - 12)*a(n-1) - 2*(n-2)*(2*n-3)*(17*n^2 + 6*n + 1)*a(n-2). - _Vaclav Kotesovec_, Jul 05 2014

%F a(n) ~ sqrt(95+393/sqrt(17)) * ((71+17*sqrt(17))/16)^n / (4*sqrt(2*Pi) * n^(3/2)). - _Vaclav Kotesovec_, Jul 05 2014

%o (PARI) {a(n)=if(n==0,1,sum(j=0,n, if(j==0,1,sum(k=0,j,2*binomial(j,k)*binomial(2*j+k,k-1)/j))* if(n-j==0,1,sum(k=0,n-j,2*binomial(n-j,k)*binomial(2*n-2*j+k,k-1)/(n-j)))))}

%Y Cf. A003169, A100324, A100326, A100327.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 17 2004

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)