A358953
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1).
Original entry on oeis.org
1, 3, 21, 159, 1369, 12131, 111489, 1042310, 9878188, 94345595, 905236045, 8698907855, 83509981377, 798911473287, 7596665295846, 71585365842419, 666055801137389, 6089025714101416, 54304588402962717, 467144137463862047, 3798557443794080777, 27983895459969702990
Offset: 0
G.f.: A(x) = 1 + 3*x + 21*x^2 + 159*x^3 + 1369*x^4 + 12131*x^5 + 111489*x^6 + 1042310*x^7 + 9878188*x^8 + 94345595*x^9 + 905236045*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(3*n) * (x^n - 2*Ser(A))^(4*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358954
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(4*n) * (x^n - 2*A(x))^(5*n+1).
Original entry on oeis.org
1, 4, 36, 384, 4568, 57920, 768760, 10543120, 148247390, 2125715618, 30965114225, 456956616284, 6817011617601, 102640570550600, 1557716916728198, 23804070258610024, 365964582592739540, 5656501536118793076, 87846324474413129008, 1370097609728212588634, 21451062781643458337802
Offset: 0
G.f.: A(x) = 1 + 4*x + 36*x^2 + 384*x^3 + 4568*x^4 + 57920*x^5 + 768760*x^6 + 10543120*x^7 + 148247390*x^8 + 2125715618*x^9 + 30965114225*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(4*n) * (x^n - 2*Ser(A))^(5*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358955
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(5*n) * (x^n - 2*A(x))^(6*n+1).
Original entry on oeis.org
1, 5, 55, 715, 10285, 157577, 2521339, 41635879, 704264465, 12139738505, 212475103777, 3765897874074, 67454279084444, 1219122315546851, 22204489538545069, 407150017658467685, 7509869807043464691, 139245172845883281403, 2593887890033997265241, 48521833007161546858193
Offset: 0
G.f.: A(x) = 1 + 5*x + 55*x^2 + 715*x^3 + 10285*x^4 + 157577*x^5 + 2521339*x^6 + 41635879*x^7 + 704264465*x^8 + 12139738505*x^9 + 212475103777*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(5*n) * (x^n - 2*Ser(A))^(6*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358956
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(6*n) * (x^n - 2*A(x))^(7*n+1).
Original entry on oeis.org
1, 6, 78, 1196, 20280, 366288, 6908744, 134492752, 2681961056, 54504790720, 1124768357872, 23505633975616, 496452504891320, 10580216111991080, 227237269499825185, 4913552644294206262, 106877300690757456293, 2336971970184440328572, 51339570414117180476064
Offset: 0
G.f.: A(x) = 1 + 6*x + 78*x^2 + 1196*x^3 + 20280*x^4 + 366288*x^5 + 6908744*x^6 + 134492752*x^7 + 2681961056*x^8 + 54504790720*x^9 + 1124768357872*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(6*n) * (x^n - 2*Ser(A))^(7*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358957
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(7*n) * (x^n - 2*A(x))^(8*n+1).
Original entry on oeis.org
1, 7, 105, 1855, 36225, 753319, 16356809, 366518975, 8412321985, 196761671175, 4672976571753, 112386313863327, 2731613284143345, 66992673654966087, 1655756220596437601, 41199365822954474670, 1031225066096367871764, 25947188077245338061147, 655925022779049206277461
Offset: 0
G.f.: A(x) = 1 + 7*x + 105*x^2 + 1855*x^3 + 36225*x^4 + 753319*x^5 + 16356809*x^6 + 366518975*x^7 + 8412321985*x^8 + 196761671175*x^9 + 4672976571753*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(7*n) * (x^n - 2*Ser(A))^(8*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358958
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(8*n) * (x^n - 2*A(x))^(9*n+1).
Original entry on oeis.org
1, 8, 136, 2720, 60112, 1414400, 34744192, 880722944, 22866372480, 604987038208, 16252230833792, 442118711113216, 12154717695451712, 337169716435693120, 9425612400257630864, 265272780558100130464, 7510038750103097772890, 213729057394800722424678, 6110972702751703321123745
Offset: 0
G.f.: A(x) = 1 + 8*x + 136*x^2 + 2720*x^3 + 60112*x^4 + 1414400*x^5 + 34744192*x^6 + 880722944*x^7 + 22866372480*x^8 + 604987038208*x^9 + 16252230833792*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(8*n) * (x^n - 2*Ser(A))^(9*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A358959
a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(9*n) * (x^n - 2*A(x))^(10*n+1).
Original entry on oeis.org
1, 9, 171, 3819, 94221, 2474541, 67842255, 1919233719, 55608288057, 1641837803793, 49218744365683, 1494112796918051, 45836491198618821, 1418839143493455861, 44259772786526485527, 1389967891240928450511, 43910122539568806384513, 1394423517592589134138485
Offset: 0
G.f.: A(x) = 1 + 9*x + 171*x^2 + 3819*x^3 + 94221*x^4 + 2474541*x^5 + 67842255*x^6 + 1919233719*x^7 + 55608288057*x^8 + 1641837803793*x^9 + 49218744365683*x^10 + ...
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{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^(9*n) * (x^n - 2*Ser(A))^(10*n+1) ), #A-1)/2);A[n+1]}
for(n=0,25,print1(a(n),", "))
A361766
Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * (1 - x^n/A(-x))^(n+2).
Original entry on oeis.org
1, 1, 2, 5, 12, 27, 57, 123, 280, 666, 1614, 3955, 9733, 23949, 58967, 145844, 363137, 910339, 2295192, 5811070, 14754567, 37542078, 95715596, 244567665, 626388406, 1608131393, 4137707994, 10667045757, 27546269363, 71241831762, 184508259405, 478501423792
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 27*x^5 + 57*x^6 + 123*x^7 + 280*x^8 + 666*x^9 + 1614*x^10 + 3955*x^11 + 9733*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 * (1 - (-x)^m/Ser(A))^(m+2) ), #A-3));A[n+1]}
for(n=0,35,print1(a(n),", "))
Showing 1-8 of 8 results.
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