A303058
G.f. A(x) satisfies: A(x) = Sum_{n>=0} (1+x)^(n^2) * x^n / A(x)^n.
Original entry on oeis.org
1, 1, 1, 2, 5, 16, 61, 259, 1228, 6284, 34564, 201978, 1246652, 8084728, 54862377, 388266809, 2857708840, 21822753453, 172550972216, 1410144139982, 11892084248959, 103343300813517, 924223611649636, 8496346816801059, 80201063980292729, 776585923239589681, 7706568335863727817, 78311132374535936605
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 16*x^5 + 61*x^6 + 259*x^7 + 1228*x^8 + 6284*x^9 + 34564*x^10 + 201978*x^11 + 1246652*x^12 + ...
such that
A(x) = 1 + (1+x)*x/A(x) + (1+x)^4*x^2/A(x)^2 + (1+x)^9*x^3/A(x)^3 + (1+x)^16*x^4/A(x)^4 + (1+x)^25*x^5/A(x)^5 + (1+x)^36*x^6/A(x)^6 + ...
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{a(n) = my(A=[1]); for(i=1,n, A = concat(A,0); A[#A] = Vec(sum(n=0,#A, ((1+x)^n +x*O(x^#A))^n * x^n/Ser(A)^n ) )[#A] );A[n+1]}
for(n=0,30,print1(a(n),", "))
A301927
G.f. A(x) satisfies: x = Sum_{n>=1} x^n / ( (1-x)^(n^2) * A(x)^n ).
Original entry on oeis.org
1, 2, 4, 9, 24, 77, 294, 1296, 6403, 34644, 201932, 1253513, 8219110, 56578239, 406990651, 3048202700, 23700070773, 190830842843, 1588016365186, 13633603416558, 120574656241999, 1097006289005674, 10255338612462641, 98403208150304070, 968186766428157206, 9759036265967791137, 100690787844977985900, 1062601625749170026894, 11461320511629994319890
Offset: 0
G.f.: A(x) = 1 + 2*x + 4*x^2 + 9*x^3 + 24*x^4 + 77*x^5 + 294*x^6 + 1296*x^7 + 6403*x^8 + 34644*x^9 + 201932*x^10 + 1253513*x^11 + 8219110*x^12 + ...
such that
x = x/((1-x)*A(x)) + x^2/((1-x)^4*A(x)^2) + x^3/((1-x)^9*A(x)^3) + x^4/((1-x)^16*A(x)^4) + x^5/((1-x)^25*A(x)^5) + x^6/((1-x)^36*A(x)^6) + x^7/((1-x)^49*A(x)^7) + x^8/((1-x)^64*A(x)^8) + ...
-
{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = Vec(sum(n=0, #A, x^n/(((1-x)^n +x*O(x^#A))^n * Ser(A)^n) ) )[#A+1] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
A320954
G.f. A(x) satisfies: 1/(1-x) = Sum_{n>=0} (1+x)^(n^2) * x^n / A(x)^n.
Original entry on oeis.org
1, 1, 2, 5, 14, 50, 200, 919, 4633, 25361, 148606, 923394, 6043996, 41447150, 296571213, 2206965193, 17034374165, 136066491764, 1122656493744, 9552206133005, 83695193972045, 754199756930791, 6981787930209535, 66327351641879318, 646031757787129761, 6445726513363688990, 65825739028009602120, 687540665329016479660
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 50*x^5 + 200*x^6 + 919*x^7 + 4633*x^8 + 25361*x^9 + 148606*x^10 + 923394*x^11 + 6043996*x^12 + ...
such that
1/(1-x) = 1 + (1+x)*x/A(x) + (1+x)^4*x^2/A(x)^2 + (1+x)^9*x^3/A(x)^3 + (1+x)^16*x^4/A(x)^4 + (1+x)^25*x^5/A(x)^5 + (1+x)^36*x^6/A(x)^6 + ...
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{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = -1 + Vec(sum(n=0, #A, ((1+x)^n +x*O(x^#A))^n * x^n/Ser(A)^n ) )[#A+1] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
Showing 1-3 of 3 results.