A371658 G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 + A(x))^2.
1, 4, 48, 784, 14784, 302976, 6555648, 147380480, 3408817152, 80592320512, 1938923790336, 47314993324032, 1168315059240960, 29136848453632000, 732857340425011200, 18569095605771632640, 473534596510970019840, 12144227894941523116032
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..694
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, (n-1)\2, 4^(n-k)*binomial(n, k)*binomial(3*n-k, n-1-2*k))/n);
Formula
a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} 4^(n-k) * binomial(n,k) * binomial(3*n-k,n-1-2*k) for n > 0.
a(n) = 2^n * A219538(n). - Seiichi Manyama, Dec 26 2024