A386263 G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - 2*x^2*A'(x)) ).
1, 3, 15, 121, 1333, 18091, 286867, 5158385, 103226313, 2269474723, 54307112951, 1404350909545, 39020894189245, 1159475912653163, 36695329075865083, 1232560854783934561, 43801551907551784721, 1642199848241650875907, 64789265823476378293855
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Keywords
Programs
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Mathematica
terms=19; A[]=1; Do[A[x]=1/( (1-x)^2 * (1 - x*A[x] - 2*x^2*A'[x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 17 2025 *)
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;
Formula
a(n) = n + 1 + n * Sum_{k=0..n-1} a(k) * a(n-1-k).
a(n) = n + 1 + Sum_{k=0..n-1} (1 + 2*k) * a(k) * a(n-1-k).