A088131 a(n) equals the square of the n-th partial sum added to twice the n-th partial sum of the squares, divided by a(n-1), for all n>=1, with a(0)=1, a(1)=1.
1, 1, 8, 29, 115, 452, 1779, 7001, 27552, 108429, 426715, 1679308, 6608803, 26008497, 102354680, 402809917, 1585231171, 6238570004, 24551470099, 96620649225, 380244026896, 1496424637485, 5889077900715, 23176067575964
Offset: 0
Keywords
Crossrefs
Cf. A088132.
Programs
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PARI
a(0)=1; a(1)=1; for(n=2,30, a(n)=(sum(k=0,n-1,a(k))^2 + 2*sum(k=0,n-1,a(k)^2))/a(n-1))
Formula
a(n)=4a(n-1)-a(n-3) for n>3; G.f.: A(x)=(1-3x+4x^2-2x^3)/(1-4x+x^3).