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).

1, 2, 6, 16, 130, 636, 5712, 34336, 811458, 7151380, 113034746, 1049982792, 25276020640, 293841338896, 5712436923000, 68827002466176, 3739997267623490, 60752008945662372, 1718332635327516238, 26832922324005759560, 1099199814287516279394

Offset: 0

Author

Paul D. Hanna, Oct 10 2008

Keywords

• nonn

Comments

The g.f. of A144691(n) = a(n)/(n+1) appears to have an interesting functional interpretation.

For a fixed n, the sequence of [x^(2^m+n)] B(x)^(n+1), m=0,1,2,... seems to stabilize at m = n + A023416(n). [From Max Alekseyev, Dec 19 2011]

Links

• Max Alekseyev, Table of n, a(n) for n = 0..27

Crossrefs

Cf. A007178, A144691, A144692, A135068, A135069, A135070, A135071.

Programs

PARI

{ 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)) }

Formula

a(n) = (n+1)*A144691(n).

Extensions

a(14), a(15) corrected and a(16)-a(23) added by Max Alekseyev, May 03 2011

a(24)-a(27) in b-file from Max Alekseyev, Dec 19 2011