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).

1, 1, 1, 2, 5, 11, 51, 246, 897, 13526, 115631, 614681, 8739556, 89877217, 596072842

Offset

0,4

Comments

The expansion of A(x/(1+x))/(1+x) appears to be a power series in x^3.

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = A277040(n)/(n+1).

Equals the binomial transform of A277043.

Example

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.

Prog

(PARI) { 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), ", "))

Crossrefs

Cf. A144691, A277040, A277042, A277043.

Sequence in context: A285809 A089609 A362525 * A087185 A127010 A140547

Adjacent sequences: A277038 A277039 A277040 * A277042 A277043 A277044

Keyword

nonn,more

Author

Paul D. Hanna, Sep 25 2016

Status

approved