A384821
G.f. A(x) satisfies -1/x = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+2).
Original entry on oeis.org
1, 2, 5, 22, 91, 416, 1978, 9738, 49181, 253572, 1328528, 7053672, 37866294, 205188765, 1120824743, 6165155890, 34119043994, 189839648588, 1061344406923, 5959197795092, 33588952625106, 189986944364176, 1078034452020854, 6134848540680166, 35005230073846833, 200229444332667654
Offset: 0
G.f.: A(x) = 1 + 2*x + 5*x^2 + 22*x^3 + 91*x^4 + 416*x^5 + 1978*x^6 + 9738*x^7 + 49181*x^8 + 253572*x^9 + 1328528*x^10 + ...
SPECIFIC VALUES.
A(t) = 2 at t = 0.162924020448782314256916956456618618555937137963260...
A(t) = 9/5 at t = 0.15713093477961462528780113190237390843002535981643...
A(t) = 8/5 at t = 0.14467881602482935797425598908263109752382579929421...
A(t) = 3/2 at t = 0.13461615563760120581581313629107981605312435881819...
A(t) = 4/3 at t = 0.10915621052082212882653574706851509193398803739915...
A(1/7) = 1.5793911503434252677981671019480264164820055324466...
A(1/8) = 1.4268350851974567615394958810072981944850896947894...
A(1/9) = 1.3435470274993477728207146854713823085043981519155...
A(1/10) = 1.2892440747830023480637465318368592024118039394009...
A(1/11) = 1.2505209808081799972669805855553805055082827658365...
-
{a(n) = my(A=[1,2,0]); for(i=1, n, A = concat(A, 0);
A[#A-1] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+2) ), #A-4)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384823
G.f. A(x) satisfies -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).
Original entry on oeis.org
1, 1, 4, 28, 173, 1262, 9593, 75928, 618342, 5149640, 43650123, 375347585, 3266282211, 28709930633, 254526671024, 2273271614848, 20435110855838, 184745786960642, 1678668998195885, 15321962225034079, 140418372363945954, 1291587696225346583, 11919771215919819476, 110338977972166474055
Offset: 0
G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 173*x^4 + 1262*x^5 + 9593*x^6 + 75928*x^7 + 618342*x^8 + 5149640*x^9 + 43650123*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-3] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+6) ), #A-16)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384824
G.f. A(x) satisfies 1/x^19 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+8).
Original entry on oeis.org
1, 1, 5, 38, 319, 2871, 27507, 273925, 2808973, 29457644, 314470771, 3405995019, 37334767867, 413397265017, 4617060957512, 51951448775027, 588371324004508, 6701761863368579, 76723673176823126, 882342098781937683, 10188542630975395255, 118082022786322630334, 1373108879790849494070
Offset: 0
G.f.: A(x) = 1 + x + 5*x^2 + 38*x^3 + 319*x^4 + 2871*x^5 + 27507*x^6 + 273925*x^7 + 2808973*x^8 + 29457644*x^9 + 314470771*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-4] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+8) ), #A-25)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384825
G.f. A(x) satisfies -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).
Original entry on oeis.org
1, 1, 6, 54, 542, 5955, 69114, 835140, 10391843, 132262619, 1713785727, 22531557603, 299817809184, 4030217936308, 54646151953660, 746513545616000, 10264746883787021, 141955200254335604, 1973170863256461516, 27551902179444882489, 386288077655575999571, 5435910477286670671340
Offset: 0
G.f.: A(x) = 1 + x + 6*x^2 + 54*x^3 + 542*x^4 + 5955*x^5 + 69114*x^6 + 835140*x^7 + 10391843*x^8 + 132262619*x^9 + 1713785727*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-5] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+10) ), #A-36)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384826
G.f. A(x) satisfies 1/x^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).
Original entry on oeis.org
1, 1, 7, 73, 861, 11112, 151828, 2159179, 31627690, 473917665, 7230164079, 111926802631, 1753762735460, 27760507986844, 443257137593369, 7130838718144623, 115469073853104486, 1880570694656739472, 30784302913287253256, 506228988080918570208, 8358750672258509735440, 138528877561300962357350
Offset: 0
G.f.: A(x) = 1 + x + 7*x^2 + 73*x^3 + 861*x^4 + 11112*x^5 + 151828*x^6 + 2159179*x^7 + 31627690*x^8 + 473917665*x^9 + 7230164079*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-6] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+12) ), #A-49)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384827
G.f. A(x) satisfies -1/x^55 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+14).
Original entry on oeis.org
1, 1, 8, 95, 1288, 19116, 300511, 4918268, 82918049, 1430142380, 25115651237, 447578072658, 8073426806649, 147122009148252, 2704441907759235, 50088849266618466, 933792151007378231, 17509062834076661230, 329985690688947517626, 6247533413700369107192, 118768564127167799819733
Offset: 0
G.f.: A(x) = 1 + x + 8*x^2 + 95*x^3 + 1288*x^4 + 19116*x^5 + 300511*x^6 + 4918268*x^7 + 82918049*x^8 + 1430142380*x^9 + 25115651237*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-7] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+14) ), #A-64)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A384828
G.f. A(x) satisfies 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).
Original entry on oeis.org
1, 1, 9, 120, 1839, 30862, 548783, 10160786, 193811734, 3782270289, 75158649892, 1515578476370, 30935212293083, 637920390487505, 13269865608471203, 278121828806207328, 5867506406619195047, 124502776024601555996, 2655381364988431518262, 56892952987400631546208, 1223972213493916563960331
Offset: 0
G.f.: A(x) = 1 + x + 9*x^2 + 120*x^3 + 1839*x^4 + 30862*x^5 + 548783*x^6 + 10160786*x^7 + 193811734*x^8 + 3782270289*x^9 + 75158649892*x^10 + ...
-
{a(n) = my(A=[1,1,0,0,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-8] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+16) ), #A-81)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
Showing 1-7 of 7 results.