A361772
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(2*n-1).
Original entry on oeis.org
1, 1, 8, 61, 600, 6072, 65804, 733435, 8415694, 98529785, 1173278329, 14162417506, 172914841649, 2131621288494, 26495818020038, 331706510158239, 4178800564364333, 52935845003315662, 673878770026778330, 8616336680850069832, 110606714769468383785, 1424933340070339610543
Offset: 0
G.f.: A(x) = 1 + x + 8*x^2 + 61*x^3 + 600*x^4 + 6072*x^5 + 65804*x^6 + 733435*x^7 + 8415694*x^8 + 98529785*x^9 + 1173278329*x^10 + ...
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{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(2*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A361773
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(3*n-1).
Original entry on oeis.org
1, 2, 34, 677, 15660, 393790, 10433402, 286990626, 8117763488, 234635708480, 6899771599141, 205768408153474, 6208628685564955, 189188990142419693, 5813805339043713267, 179968235623379467274, 5606627898452185950618, 175650401043239524832783, 5530500462355496324862920
Offset: 0
G.f.: A(x) = 1 + 2*x + 34*x^2 + 677*x^3 + 15660*x^4 + 393790*x^5 + 10433402*x^6 + 286990626*x^7 + 8117763488*x^8 + 234635708480*x^9 + 6899771599141*x^10 + ...
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{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(3*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A361771
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(n-1).
Original entry on oeis.org
1, 1, 1, 7, 28, 89, 421, 1898, 7912, 36412, 169960, 779139, 3668210, 17486938, 83333003, 400956919, 1943928504, 9455346485, 46225027071, 227066384875, 1119123274755, 5534782142253, 27463607765186, 136652474592260, 681728348606011, 3409395265172439, 17088672210734316
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 7*x^3 + 28*x^4 + 89*x^5 + 421*x^6 + 1898*x^7 + 7912*x^8 + 36412*x^9 + 169960*x^10 + 779139*x^11 + 3668210*x^12 + ...
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{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A363114
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(4*n-1).
Original entry on oeis.org
1, 4, 138, 6571, 353935, 20694945, 1276853497, 81834405039, 5395444806588, 363600236084796, 24933767742193052, 1734273108108910743, 122058422998192278797, 8676376795137864622232, 622018188741046650309066, 44922343315319150402783783, 3265215115112327274815579250
Offset: 0
G.f.: A(x) = 1 + 4*x + 138*x^2 + 6571*x^3 + 353935*x^4 + 20694945*x^5 + 1276853497*x^6 + 81834405039*x^7 + 5395444806588*x^8 + ...
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{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff(-1 + sum(m=-#A, #A, x^m * (2*Ser(A) - x^m)^(4*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
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{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff(1 - sum(m=-#A, #A, x^(4*m^2)/(1 - 2*Ser(A)*x^m)^(4*m+1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
Showing 1-4 of 4 results.