A301931
G.f. A(x) satisfies: A(x) = x*(1 + A(x)*A'(x)) / (1 - A(x)*A'(x)).
Original entry on oeis.org
1, 2, 14, 154, 2186, 36930, 712158, 15295602, 360155378, 9196938274, 252714360398, 7428201595178, 232480106673562, 7717715629942274, 270896581615492926, 10025955123898058082, 390290027013023089122, 15945008348985522925890, 682270367930391378957198, 30518971384549282782489786, 1424657384555111198491140138, 69290703924209121823629630018
Offset: 1
G.f.: A(x) = x + 2*x^2 + 14*x^3 + 154*x^4 + 2186*x^5 + 36930*x^6 + 712158*x^7 + 15295602*x^8 + 360155378*x^9 + 9196938274*x^10 + ...
RELATED SERIES.
A(x)*A'(x) = x + 6*x^2 + 64*x^3 + 910*x^4 + 15552*x^5 + 304206*x^6 + 6627840*x^7 + 158162238*x^8 + 4087933120*x^9 + 113539676470*x^10 + ...
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{a(n) = my(L=x); for(i=1,n, L = x*(1 + L'*L)/(1 - L'*L +x*O(x^n)) ); polcoeff(L,n)}
for(n=1,30,print1(a(n),", "))
A301932
G.f. A(x) satisfies: A(x) = x*(1 + 3*A(x)*A'(x)) / (1 + A(x)*A'(x)).
Original entry on oeis.org
1, 2, 10, 74, 710, 8322, 115018, 1828962, 32852526, 657188258, 14477811178, 348100068698, 9067809569750, 254354791759298, 7642986480897930, 244923580410697938, 8337728465913016926, 300482221889444825154, 11429089791630856291018, 457542303069698601849194, 19230862148761320966737254, 846710680545018639230252418
Offset: 1
G.f.: A(x) = x + 2*x^2 + 10*x^3 + 74*x^4 + 710*x^5 + 8322*x^6 + 115018*x^7 + 1828962*x^8 + 32852526*x^9 + 657188258*x^10 + ...
such that A = A(x) satisfies: A = x*(1 + 3*A*A')/(1 + A*A').
RELATED SERIES.
A(x)*A'(x) = x + 6*x^2 + 48*x^3 + 470*x^4 + 5448*x^5 + 73374*x^6 + 1132000*x^7 + 19752822*x^8 + 385285080*x^9 + 8311631702*x^10 + ...
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{a(n) = my(L=x); for(i=1,n, L = x*(1 + 3*L'*L)/(1 + L'*L +x*O(x^n)) ); polcoeff(L,n)}
for(n=1,30,print1(a(n),", "))
A301933
G.f. A(x) satisfies: A(x) = x*(1 + 4*A(x)*A'(x)) / (1 + A(x)*A'(x)).
Original entry on oeis.org
1, 3, 24, 291, 4596, 88230, 1979088, 50570823, 1446341388, 45706515546, 1580322048288, 59318131995822, 2401809350808552, 104347127373249036, 4842030589556434656, 239028273094016840223, 12508863342589554285372, 691783629316556340447570, 40316336264435949765811968
Offset: 1
G.f.: A(x) = x + 3*x^2 + 24*x^3 + 291*x^4 + 4596*x^5 + 88230*x^6 + 1979088*x^7 + 50570823*x^8 + 1446341388*x^9 + 45706515546*x^10 + ...
such that A = A(x) satisfies: A = x*(1 + 4*A*A')/(1 + A*A').
Odd coefficients in A(x) seem to occur only for x^(2^k), k>=0.
RELATED SERIES.
A(x)*A'(x) = x + 9*x^2 + 114*x^3 + 1815*x^4 + 34542*x^5 + 763014*x^6 + 19171380*x^7 + 539667387*x^8 + 16817885070*x^9 + 574647250650*x^10 + ...
Odd coefficients in A(x)*A'(x) also seem to occur only for x^(2^k), k>=0.
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{a(n) = my(L=x); for(i=1,n, L = x*(1 + 4*L'*L)/(1 + L'*L +x*O(x^n)) ); polcoeff(L,n)}
for(n=1,30,print1(a(n),", "))
Showing 1-3 of 3 results.
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