A144691
Limit of the coefficient of x^(2^m+n) in B(x)^(n+1)/(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
Original entry on oeis.org
1, 1, 2, 4, 26, 106, 816, 4292, 90162, 715138, 10275886, 87498566, 1944309280, 20988667064, 380829128200, 4301687654136, 219999839271970, 3375111608092354, 90438559754079802, 1341646116200287978, 52342848299405537114, 921821277222438350170
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 26*x^4 + 106*x^5 + 816*x^6 +...
A(x/G(x)) = G(x) = x/Series_Reversion[x*A(x)], where
G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
and G(x) appears to continue with only even powers of x (cf. A144692).
The inverse binomial transform forms the g.f. of A202582:
A(x/(1+x))/(1+x) = 1 + x^2 + 19*x^4 + 515*x^6 + 74383*x^8 + 6816465*x^10 +...+ A202582(n)*x^n +...
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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)/(n+1),2^m+n)) }
a(14), a(15) corrected and a(16)-a(23) added by
Max Alekseyev, May 03 2011
A166488
Number of transpose-isomorphism classes of SOLSSOMs of order n.
Original entry on oeis.org
31, 749, 0, 1210622, 1248307242, 640121719688, 0
Offset: 4
- A.P. Burger, M.P. Kidd and J.H. van Vuuren, Enumeration of self-orthogonal Latin squares with symmetric orthogonal mates, Submitted to LitNet Akademies (Natuurwetenskappe)
Class name and definition corrected by
Martin P Kidd, Nov 01 2010
A277040
Limit of the coefficient of x^(3^m + n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(3^k).
Original entry on oeis.org
1, 2, 3, 8, 25, 66, 357, 1968, 8073, 135260, 1271941, 7376172, 113614228, 1258281038, 8941092630
Offset: 0
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{ a(n) = local(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), 3^m+n) }
for(n=0,15,print1(a(n),", "))
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.
Showing 1-4 of 4 results.
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