A386209
G.f. A(x) satisfies A(x) = 1/(1-x)^2 + x^2 * (d/dx A(x)^2).
Original entry on oeis.org
1, 2, 7, 40, 329, 3474, 44127, 650144, 10862273, 202632498, 4172689415, 94010964072, 2300682029417, 60787775220578, 1725027567563263, 52338601112555648, 1691028812744005697, 57973475215478590626, 2102150579452302435655, 80389277428829219813864
Offset: 0
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a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+(i-1)*sum(j=0, i-1, v[j+1]*v[i-j])); v;
A386212
G.f. A(x) satisfies A(x) = 1/(1-x)^3 + x^2*A(x)*A'(x).
Original entry on oeis.org
1, 3, 9, 37, 207, 1455, 12073, 113949, 1196499, 13778155, 172269777, 2321464773, 33524717911, 516428180631, 8453096463321, 146532991389613, 2682216423470763, 51706945300407315, 1047284621276095729, 22237895367773398821, 494041637873385734127, 11462206075715032723903
Offset: 0
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a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+(i-1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
A386229
G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - x^2*A'(x)) ).
Original entry on oeis.org
1, 3, 12, 70, 535, 4908, 51478, 600584, 7662285, 105684465, 1563183259, 24645719004, 412279514088, 7290426692472, 135862518564330, 2661378323466016, 54675576786754501, 1175673956931922257, 26411686616265112230, 618863341216409971750, 15101129008183181824938
Offset: 0
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terms = 21; A[] = 1; Do[A[x] = 1/((1-x)^2(1-x*A[x]-x^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 16 2025 *)
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a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(i+1)*(1+sum(j=0, i-1, v[j+1]*v[i-j])/2)); v;
Showing 1-3 of 3 results.