A357791
a(n) = coefficient of x^n in A(x) such that: x = Sum_{n=-oo..+oo} x^n * (1 - x^n * A(-x)^n)^n.
Original entry on oeis.org
1, 1, 2, 5, 21, 88, 377, 1654, 7424, 34000, 158274, 746525, 3559456, 17128250, 83078147, 405754479, 1993777057, 9849668910, 48892589632, 243739139810, 1219789105228, 6125813250402, 30862120708266, 155937956267432, 790019313067409, 4012282344217699, 20423575546661000
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 21*x^4 + 88*x^5 + 377*x^6 + 1654*x^7 + 7424*x^8 + 34000*x^9 + 158274*x^10 + 746525*x^11 + 3559456*x^12 + ...
SPECIFIC VALUES.
A(x) = 3/2 at x = 0.1850570503493984408934312903280642188437354418734...
A(1/6) = 1.3085832721715442420948608003299892250459754159045...
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{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x + sum(n=-#A, #A, (-x)^n * (1 - (-x)^n * Ser(A)^n )^n ), #A-1) ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A359922
a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (2 + x^n*A(x)^n)^n.
Original entry on oeis.org
1, 1, 4, 9, 42, 187, 775, 3470, 16085, 76521, 368274, 1791494, 8829531, 43964379, 220667042, 1115235384, 5671532510, 29004157940, 149056379047, 769368598912, 3986831368824, 20733495321171, 108175116519808, 566067951728994, 2970221822319878, 15624080964153005
Offset: 0
G.f.: A(x) = 1 + x + 4*x^2 + 9*x^3 + 42*x^4 + 187*x^5 + 775*x^6 + 3470*x^7 + 16085*x^8 + 76521*x^9 + 368274*x^10 + ...
where
x = ... + x^6*A(x)^9/(1 + 2*x^3*A(x)^3)^3 - x^2*A(x)^4/(1 + 2*x^2*A(x)^2)^2 + A(x)/(1 + 2*x*A(x)) - 1 + x*(2 + x*A(x)) - x^2*(2 + x^2*A(x)^2)^2 + x^3*(2 + x^3*A(x)^3)^3 + ... + (-1)^(n-1) * x^n * (2 + x^n*A(x)^n)^n + ...
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{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^(m-1) * x^m * (2 + (x*Ser(A))^m)^m ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A359923
a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n.
Original entry on oeis.org
1, 1, 6, 15, 69, 376, 1741, 8860, 46044, 245074, 1336538, 7337135, 40736876, 228625148, 1293530435, 7372491383, 42275811853, 243742895280, 1412310750812, 8219298313118, 48023377286364, 281592177442072, 1656522460985914, 9773791391488278, 57824226906859849
Offset: 0
G.f.: A(x) = 1 + x + 6*x^2 + 15*x^3 + 69*x^4 + 376*x^5 + 1741*x^6 + 8860*x^7 + 46044*x^8 + 245074*x^9 + 1336538*x^10 + ...
where
x = ... + x^6*A(x)^9/(1 + 3*x^3*A(x)^3)^3 - x^2*A(x)^4/(1 + 3*x^2*A(x)^2)^2 + A(x)/(1 + 3*x*A(x)) - 1 + x*(3 + x*A(x)) - x^2*(3 + x^2*A(x)^2)^2 + x^3*(3 + x^3*A(x)^3)^3 + ... + (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n + ...
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{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^(m-1) * x^m * (3 + (x*Ser(A))^m)^m ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A359669
a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(n*(n+1)) * A(x)^(n^2).
Original entry on oeis.org
1, 1, 0, 3, 6, 13, 55, 142, 429, 1495, 4538, 14894, 50279, 164189, 554402, 1883870, 6371434, 21854442, 75183191, 259137380, 899092908, 3127293679, 10907931688, 38188033950, 133998312862, 471339759941, 1662075700667, 5872497411731, 20790187564837, 73741279736768
Offset: 0
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{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^(m-1) * x^(m*(m+1)) * Ser(A)^(m^2) ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
Showing 1-4 of 4 results.
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