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
-
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
-
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;
A386230
G.f. A(x) satisfies A(x) = 1/( (1-x)^3 * (1 - x*A(x) - x^2*A'(x)) ).
Original entry on oeis.org
1, 4, 18, 114, 945, 9399, 106645, 1342028, 18409725, 272154510, 4300884555, 72225827628, 1283066570500, 24025524690426, 472822444534395, 9755834028122904, 210600429263424372, 4747647482075588598, 111583282733838959542, 2729989048854423409090, 69430953497076613542366
Offset: 0
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terms = 21; A[] = 1; Do[A[x] = 1/((1-x)^3(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]=binomial(i+2, 2)+(i+1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
Showing 1-3 of 3 results.