A361774
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, 150, 7003, 380817, 22517717, 1405927141, 91215539609, 6089092570148, 415519886498886, 28855638743197866, 2032628861705203315, 144884697917577076857, 10430845410431559928714, 757390467820895322043476, 55401570124877193188443429, 4078685155312165112343519832
Offset: 0
G.f.: A(x) = 1 + 4*x + 150*x^2 + 7003*x^3 + 380817*x^4 + 22517717*x^5 + 1405927141*x^6 + 91215539609*x^7 + 6089092570148*x^8 + ...
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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)^(4*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A363112
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, 6, 51, 470, 4716, 49350, 534115, 5929892, 67175779, 773473709, 9025907984, 106511693025, 1268898400188, 15240421643846, 184348620664449, 2243749948233175, 27459089491691552, 337685454820968084, 4170918486201555250, 51719670553572755173, 643610071084847351183
Offset: 0
G.f.: A(x) = 1 + x + 6*x^2 + 51*x^3 + 470*x^4 + 4716*x^5 + 49350*x^6 + 534115*x^7 + 5929892*x^8 + 67175779*x^9 + 773473709*x^10 + ...
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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)^(2*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^(2*m^2)/(1 - 2*Ser(A)*x^m)^(2*m+1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A363113
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, 30, 621, 14196, 351802, 9179386, 248533626, 6917835992, 196730606200, 5691264122213, 166961281712818, 4955321842136163, 148522859439511133, 4489164688548477495, 136677755757518772050, 4187859771944659634378, 129039023692329781903247, 3995878021838502688832856
Offset: 0
G.f.: A(x) = 1 + 2*x + 30*x^2 + 621*x^3 + 14196*x^4 + 351802*x^5 + 9179386*x^6 + 248533626*x^7 + 6917835992*x^8 + 196730606200*x^9 + ...
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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)^(3*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, (-1)^(m+1) * x^(3*m^2)/(1 - 2*Ser(A)*x^m)^(3*m+1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
Showing 1-3 of 3 results.