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%I #17 May 10 2020 08:37:18
%S 1,2,10,80,790,8720,103060,1275680,16326190,214280720,2868504460,
%T 39014154080,537592643740,7488960021920,105295566289960,
%U 1492291482505280,21296015905884190,305755507155234320
%N a(n)=0^n+sum{k=0..n-1, C(n+k-1,2k)*A000108(k)*3^k*2^(n-k)}
%C Hankel transform is 2^n*3^C(n+1,2)*5^C(n,2). A152601(n)=a(n+1)/2.
%H Vincenzo Librandi, <a href="/A152600/b152600.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = 2^n * (4*(n+1)*LegendreP(n+1,4) - (31*n+16)*LegendreP(n,4))/(3*n*(n-1)) for n>1. - _Mark van Hoeij_, May 27 2010
%F Recurrence: n*a(n) = 8*(2*n-3)*a(n-1) - 4*(n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) ~ sqrt(8*sqrt(15)-30)*(8+2*sqrt(15))^n/(6*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 20 2012
%t Flatten[{1,2,Table[2^n*(4*(n+1)*LegendreP[n+1,4]-(31*n+16)*LegendreP[n,4])/(3*n*(n-1)),{n,2,20}]}] (* _Vaclav Kotesovec_, Oct 20 2012 *)
%o (PARI) a(n)=if(n>1, (4*(n+1)*pollegendre(n+1,4) - (31*n+16)*pollegendre(n,4))/(3*n*(n-1))<<n, n+1) \\ _Charles R Greathouse IV_, Mar 19 2017
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 09 2008
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