A144692
G.f.: A(x) = x/Series_Reversion[x*G(x)] where A(x*G(x)) = G(x) = g.f. of A144691.
Original entry on oeis.org
1, 1, 1, 0, 17, 0, 408, 0, 69473, 0, 6018928, 0, 1363916728, 0, 219434809664, 0, 184186824259233, 0, 57411426894898072, 0, 38606038922780709192, 0, 16136153318586799828504, 0, 20401945614919621585224136, 0, 12864310266687158415460633528, 0
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
satisfies: A(x*G(x)) = G(x) = g.f. of A144691 where
G(x) = 1 + x + 2*x^2 + 4*x^3 + 26*x^4 + 106*x^5 + 816*x^6 + 4292*x^7 +...
a(14) corrected and a(16)-a(23) added by
Max Alekseyev, May 03 2011
A202582
Inverse binomial transform of A144691.
Original entry on oeis.org
1, 0, 1, 0, 19, 0, 515, 0, 74383, 0, 6816465, 0, 1457117673, 0, 241183200687, 0, 188350353304919, 0, 60855583632497865, 0, 39858196864723826583, 0, 17024263169695049621551, 0, 20817292362271689177123509, 0, 13408255577123563666760376685, 0
Offset: 0
G.f.: A(x) = 1 + x^2 + 19*x^4 + 515*x^6 + 74383*x^8 + 6816465*x^10 +...
where
x/Series_Reversion(x*A(x)) = 1 + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...+ A144692(n)*x^n +...
The g.f. G(x) of A144692 begins:
G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
where G(x) satisfies: A(x) = G(x*A(x))/(1+x) and G(x) = A(x/(G(x)-x)) + x.
A144690
Limit of the coefficient of x^(2^m+n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
Original entry on oeis.org
1, 2, 6, 16, 130, 636, 5712, 34336, 811458, 7151380, 113034746, 1049982792, 25276020640, 293841338896, 5712436923000, 68827002466176, 3739997267623490, 60752008945662372, 1718332635327516238, 26832922324005759560, 1099199814287516279394
Offset: 0
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{ a(n) = local(m=n+log(n+.5)\log(2), B=sum(k=0,m,x^(2^k)));if(n<0, 0, polcoeff((B+O(x^(2^m+n+1)))^(n+1),2^m+n)) }
a(14), a(15) corrected and a(16)-a(23) added by
Max Alekseyev, May 03 2011
A277041
Limit of the coefficient of x^(3^m + n) in B(x)^(n+1)/(n+1) as m grows, where B(x) = Sum_{k>=0} x^(3^k).
Original entry on oeis.org
1, 1, 1, 2, 5, 11, 51, 246, 897, 13526, 115631, 614681, 8739556, 89877217, 596072842
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 11*x^5 + 51*x^6 + 246*x^7 + 897*x^8 + 13526*x^9 + 115631*x^10 + 614681*x^11 + 8739556*x^12 + 89877217*x^13 + 596072842*x^14 +...
RELATED SERIES.
A(x/G(x)) = G(x) = x/Series_Reversion[x*A(x)], where
G(x) = 1 + x + x^3 + 27*x^6 + 10666*x^9 + 6174792*x^12 +...+ A277042(n)*x^n +...
and G(x) appears to continue with powers of x^3 only.
The inverse binomial transform forms the g.f. of A277043:
A(x/(1+x))/(1+x) = 1 + x^3 + 30*x^6 + 10921*x^9 + 6308995*x^12 +...+ A277043(n)*x^n +...
which also appears to continue with powers of x^3 only.
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{ a(n) = my(m=n + ceil(log(n+3)/log(3)), B=sum(k=0, m, x^(3^k))); polcoeff((B+O(x^(3^m+n+1)))^(n+1)/(n+1), 3^m+n) }
for(n=0,10,print1(a(n),", "))
Showing 1-4 of 4 results.
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