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),", "))
A277042
G.f.: A(x) = x/Series_Reversion[x*G(x)] where A(x*G(x)) = G(x) = g.f. of A277041.
Original entry on oeis.org
1, 1, 0, 1, 0, 0, 27, 0, 0, 10666, 0, 0, 6174792, 0, 0
Offset: 0
G.f.: A(x) = 1 + x + x^3 + 27*x^6 + 10666*x^9 + 6174792*x^12 +...
such that: A(x*G(x)) = G(x) = g.f. of A277041 where
G(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 +...+ A277041(n)*x^n +...
A277043
Inverse binomial transform of A277041.
Original entry on oeis.org
1, 0, 0, 1, 0, 0, 30, 0, 0, 10921, 0, 0, 6308995, 0, 0
Offset: 0
G.f.: A(x) = 1 + x^3 + 30*x^6 + 10921*x^9 + 6308995*x^12 +...
such that the binomial transform forms the g.f. of A277041:
A(x/(1-x))/(1-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 +...+ A277041(n)*x^n +...
Also, A(x/(G(x) - x)) = G(x) - x where G(x) = g.f. of A277042 where
G(x) = 1 + x + x^3 + 27*x^6 + 10666*x^9 + 6174792*x^12 +...+ A277042(n)*x^n +...
Showing 1-3 of 3 results.
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