A379763
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n * (A(x) + x^n)^(n-1).
Original entry on oeis.org
1, 8, 28, 80, 340, 2872, 23272, 150496, 878032, 5590352, 40944964, 308188080, 2214574160, 15460447160, 109979357264, 810265214336, 6054587741784, 44971580074120, 332187742343988, 2466464253968144, 18500526368526048, 139644462606436800, 1055241582609777512, 7976465101937086048
Offset: 0
G.f.: A(x) = 1 + 8*x + 28*x^2 + 80*x^3 + 340*x^4 + 2872*x^5 + 23272*x^6 + 150496*x^7 + 878032*x^8 + 5590352*x^9 + 40944964*x^10 + ...
SPECIFIC VALUES.
A(t) = 4 at t = 0.1235342678268539440746589398189578740264504317462121...
A(t) = 7/2 at t = 0.12337584148360853579899960670632890137087362247055...
A(t) = 3 at t = 0.1189669970336741794074612973623362011930913609542464...
A(t) = 8/3 at t = 0.11236236009985673845496192883838338061075287809042...
A(t) = 5/2 at t = 0.10760338088663649599824099427959331111765863368322...
A(t) = 2 at t = 0.0860421126120690497056915080654929742231128974945892...
A(t) = 5/3 at t = 0.06455762863947182072889129821695321012477178467912...
A(t) = 3/2 at t = 0.05139332682125823774630591999711573636194198482312...
A(t) = 4/3 at t = 0.03643110079983399886726516650416070970893737185267...
A(1/9) = 2.61903290816405002799089092593044410910194535029138...
A(1/10) = 2.2906610607876438864547993548373950931057028357479...
A(1/11) = 2.0918693839543664253067320311652491735792259386896...
A(1/12) = 1.9521586978927587023994157391373410559426298682696...
A(1/16) = 1.6391356345727767379864792642142307766503410761688...
A(1/20) = 1.4835552560753585028949446320205963648290177148078...
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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)^(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),", "))
A380065
G.f. A(x) satisfies 2 = Sum_{n=-oo..+oo} x^(2*n) * (A(x) - x^(2*n+1))^(n-1).
Original entry on oeis.org
1, 3, 14, 98, 785, 6702, 59968, 554872, 5266164, 50982561, 501511295, 4998413255, 50366515829, 512257729704, 5251739403578, 54216242355803, 563112825354739, 5880229017352112, 61697782946493598, 650137346153943901, 6877281106762452016, 73003969200802059386, 777423197278368997747
Offset: 0
G.f.: A(x) = 1 + 3*x + 14*x^2 + 98*x^3 + 785*x^4 + 6702*x^5 + 59968*x^6 + 554872*x^7 + 5266164*x^8 + 50982561*x^9 + 501511295*x^10 + ...
SPECIFIC VALUES.
A(t) = 11/6 at t = 0.087620332691056981136009348051386438683729069234188...
A(t) = 9/5 at t = 0.0874182043261646741149981956172218350826689730404996...
A(t) = 7/4 at t = 0.0869318434801806744979925380398173982849232718054976...
A(t) = 5/3 at t = 0.0855310829705482164598754145517095235059157760682890...
A(t) = 3/2 at t = 0.0796031658964171493942046069785384177317948916037014...
where 2 = Sum_{n=-oo..+oo} t^(2*n) * (3/2 - t^(2*n+1))^(n-1).
A(t) = 4/3 at t = 0.0669971124636040282524670754433309879051494329729690...
A(t) = 5/4 at t = 0.0567962686348021793992058668495458301112625095350602...
A(t) = 6/5 at t = 0.0489819942637972068395484924808191716360116583798063...
where 2 = Sum_{n=-oo..+oo} t^(2*n) * (6/5 - t^(2*n+1))^(n-1).
A(1/12) = 1.58752189609489937448603644291125612645131622024866...
where 2 = Sum_{n=-oo..+oo} (1/12)^(2*n) * (A(1/12) - 1/12^(2*n+1))^(n-1).
A(1/13) = 1.45355309884363897926210438733196707095664015067023...
A(1/14) = 1.37996515081773437231256208297748336847364447973019...
A(1/15) = 1.33017535921565190525655216189827503321523887201567...
A(1/16) = 1.29333445310054157832439323915232565378414742432913...
A(1/20) = 1.20602500277090859861285926459871218765300896393649...
where 2 = Sum_{n=-oo..+oo} (1/20)^(2*n) * (A(1/20) - 1/20^(2*n+1))^(n-1).
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{a(n) = my(V=[1]); for(i=1, n, V=concat(V, 0); A = Ser(V);
V[#V] = polcoef(-2 + sum(n=-#V, #V, x^(2*n) * (A - x^(2*n+1))^(n-1) ), #V-1) ); V[n+1]}
for(n=0, 30, print1(a(n), ", "))
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