A379765
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (A(x) + (-x)^n)^(2*n-1).
Original entry on oeis.org
1, 4, 16, 108, 764, 5772, 45608, 372112, 3110868, 26511720, 229465696, 2011560120, 17823251908, 159361875452, 1436070211128, 13029220181024, 118919107720504, 1091130632899108, 10058749510188900, 93119868866604632, 865350260237277984, 8069341311245971172, 75482617925071807900
Offset: 0
G.f.: A(x) = 1 + 4*x + 16*x^2 + 108*x^3 + 764*x^4 + 5772*x^5 + 45608*x^6 + 372112*x^7 + 3110868*x^8 + 26511720*x^9 + 229465696*x^10 + ...
SPECIFIC VALUES.
A(t) = 2 at t = 0.09653361905915170411984272932017391451579223633328063596...
A(t) = 3/2 at t = 0.075349068495101237164879111573650564301786145264462860...
A(t) = 4/3 at t = 0.059270539047675430011940298576693796977637316335946787...
A(t) = 5/4 at t = 0.048395689470367112406846758430274833454550275773025303...
A(1/11) = 1.7859531236503504891314901027866679467841212478816...
A(1/12) = 1.6197331904782587957364168880788048296765610762165...
A(1/13) = 1.5208322951137414977098221192098933277226208754204...
A(1/14) = 1.4524825965114467294893588185221903177323240271997...
A(1/20) = 1.2612955244894656446063844025636148211057476645966...
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{a(n) = my(V=[1]); for(i=1,n, V=concat(V,0); A = Ser(V);
V[#V] = polcoef(-2 + 4*sum(n=-#V,#V, (-1)^n * x^(2*n) * (A + (-x)^n)^(2*n-1) ),#V-1) );V[n+1]}
for(n=0,30,print1(a(n),", "))
A380068
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n * (A(x) + x^n)^(2*n-1).
Original entry on oeis.org
1, 4, 36, 312, 3440, 40956, 518160, 6806320, 92021528, 1271748364, 17886165344, 255159368504, 3683262020928, 53700117957756, 789606760314200, 11696040806690484, 174362944317804916, 2614112736300210308, 39388817610142696848, 596167096482669128248, 9059675614901834999980, 138177866602598729509112
Offset: 0
G.f.: A(x) = 1 + 4*x + 36*x^2 + 312*x^3 + 3440*x^4 + 40956*x^5 + 518160*x^6 + 6806320*x^7 + 92021528*x^8 + 1271748364*x^9 + 17886165344*x^10 + ...
SPECIFIC VALUES.
A(t) = 9/5 at t = 0.060810040367940244892240134748250077713967840944862...
A(t) = 7/4 at t = 0.060471316741109796362890999165339625209169541570118...
A(t) = 5/3 at t = 0.059455864011187363622702920671351845740910151873822...
A(t) = 3/2 at t = 0.055175405333610355588278758628977431335363340728879...
A(t) = 4/3 at t = 0.046413573549935696160990703887268428961721362286826...
A(t) = 5/4 at t = 0.039506911682991228951042053988737197176348217600170...
A(1/17) = 1.6311797797272774131428286483151621703548116404225...
A(1/18) = 1.5105106929462926658533664976702138681313516080377...
A(1/20) = 1.3892813212708752419341068817323469222865996600644...
A(1/25) = 1.2551873360504999226413532789756472196341294007207...
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{a(n) = my(V=[1]); for(i=1,n, V = concat(V,0); A = Ser(V);
V[#V] = polcoef(-2 + 4*sum(n=-#V,#V, x^n * (A + x^n)^(2*n-1) ),#V-1) ); V[n+1]}
for(n=0,30,print1(a(n),", "))
A380712
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(2*n) * (A(x) + x^n)^(n-1).
Original entry on oeis.org
1, 8, 84, 1040, 14220, 207416, 3163352, 49838112, 804826128, 13251624272, 221630530572, 3754763811696, 64301286803888, 1111314020855608, 19358763742909840, 339542985410593024, 5991328544544083368, 106282296849129147080, 1894330721630908390908, 33907409814314990430864
Offset: 0
G.f.: A(x) = 1 + 8*x + 84*x^2 + 1040*x^3 + 14220*x^4 + 207416*x^5 + 3163352*x^6 + 49838112*x^7 + 804826128*x^8 + 13251624272*x^9 + ...
where 1/2 = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(2*n) * (A(x) + x^n)^(n-1).
SPECIFIC VALUES.
A(t) = 11/4 at t = 0.0516760605367732994895781933476882835083123366991550...
A(t) = 5/2 at t = 0.0512706205731010752236248787488564353175797944139758...
A(t) = 9/4 at t = 0.0500962358404660270765237205868976107655318520352114...
A(t) = 2 at t = 0.0477293025632112771125356682128360981725295094219849155...
A(1/20) = 2.23597314331862522198845196504910911754398888561681...
A(1/21) = 1.99138007575616089662630287849407074435849433028712...
A(1/22) = 1.84963311768563536747915607573430165080208182054100...
A(1/23) = 1.75061850078240549448668878592242454463377302943692...
A(1/24) = 1.67559723922061838865975191745342891467177127438988...
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{a(n) = my(V=[1]); for(i=1, n, V=concat(V, 0); A = Ser(V);
V[#V] = polcoef(2 + 4*sum(n=-#V, #V, (-1)^n * x^(2*n) * (A + x^n)^(n-1) ), #V-1) ); V[n+1]}
for(n=0, 30, print1(a(n), ", "))
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