A386210 G.f. A(x) satisfies A(x) = 1/(1-x)^3 + x^2 * (d/dx A(x)^2).
1, 3, 12, 76, 687, 7917, 108928, 1725768, 30796797, 609902671, 13260956196, 313951142508, 8039710476955, 221467222589241, 6531522562100448, 205381223316464464, 6860540121003113913, 242651957254699927803, 9060531236377877408956, 356208300597443254526892
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+(i-1)*sum(j=0, i-1, v[j+1]*v[i-j])); v;
Formula
a(n) = binomial(n+2,2) + (n-1) * Sum_{k=0..n-1} a(k) * a(n-1-k).
a(n) = binomial(n+2,2) + 2 * Sum_{k=0..n-1} k * a(k) * a(n-1-k).