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
-
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;
A386208
G.f. A(x) satisfies A(x) = 1/(1-x) + x^2 * (d/dx A(x)^2).
Original entry on oeis.org
1, 1, 3, 15, 109, 1029, 11831, 159595, 2466073, 42920585, 830791243, 17706459431, 412116616517, 10403094478669, 283137307529727, 8266131486719107, 257710382446835761, 8546074646120275473, 300384437888406796051, 11155675460369469443263, 436506923733804200244509
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=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
-
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;
A386264
G.f. A(x) satisfies A(x) = 1/( (1-x)^3 * (1 - x*A(x) - 2*x^2*A'(x)) ).
Original entry on oeis.org
1, 4, 22, 190, 2239, 32431, 546832, 10414132, 219845677, 5079617326, 127292440606, 3435881715553, 99351006910147, 3063829146597493, 100385767850729656, 3483114440490487576, 127610457725933245753, 4923678697863463464970, 199592119100636938629838
Offset: 0
-
terms=19; A[]=1; Do[A[x]=1/( (1-x)^3 * (1 - x*A[x] - 2*x^2*A'[x]) )+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 17 2025 *)
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;
Showing 1-4 of 4 results.