A386210
G.f. A(x) satisfies A(x) = 1/(1-x)^3 + x^2 * (d/dx A(x)^2).
Original entry on oeis.org
1, 3, 12, 76, 687, 7917, 108928, 1725768, 30796797, 609902671, 13260956196, 313951142508, 8039710476955, 221467222589241, 6531522562100448, 205381223316464464, 6860540121003113913, 242651957254699927803, 9060531236377877408956, 356208300597443254526892
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)*sum(j=0, i-1, v[j+1]*v[i-j])); v;
A386211
G.f. A(x) satisfies A(x) = 1/(1-x)^2 + x^2*A(x)*A'(x).
Original entry on oeis.org
1, 2, 5, 18, 89, 556, 4127, 35084, 334049, 3510574, 40300769, 501455462, 6721438253, 96561557816, 1480441163151, 24132225315816, 416852189961737, 7607668036964506, 146296367990498941, 2957053490913146762, 62682940163232269033, 1390605993609167492932
Offset: 0
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terms = 22; A[] = 1; Do[A[x] = 1/(1-x)^2+x^2*A[x]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+(i-1)/2*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
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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;
A386263
G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - 2*x^2*A'(x)) ).
Original entry on oeis.org
1, 3, 15, 121, 1333, 18091, 286867, 5158385, 103226313, 2269474723, 54307112951, 1404350909545, 39020894189245, 1159475912653163, 36695329075865083, 1232560854783934561, 43801551907551784721, 1642199848241650875907, 64789265823476378293855
Offset: 0
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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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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;
Showing 1-4 of 4 results.