A379171 G.f. A(x) satisfies A(x) = (1 + x)/(1 - x*A(x))^3.
1, 4, 21, 139, 1021, 8010, 65708, 556751, 4834686, 42800265, 384832083, 3504693519, 32261240127, 299685628629, 2805773759322, 26448278629697, 250806022116194, 2390973659474304, 22901157688878983, 220279614235505630, 2126890041331033797, 20606993367985131716
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n-k+1, k)*binomial(4*n-4*k+2, n-k)/(n-k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(4*n-4*k+2,n-k)/(n-k+1).