A184512 G.f.: exp( Sum_{n>=1} (x^n/n)/sqrt(1 - 2*(2*x)^n) ).

1, 1, 3, 9, 33, 115, 445, 1653, 6445, 24783, 97181, 379105, 1495607, 5884239, 23289639, 92143819, 365700023, 1451737985, 5774284819, 22976698471, 91541016133, 364883522809, 1455637611901, 5809643314425, 23201023852083

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

Logarithmic derivative yields A184513.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 33*x^4 + 115*x^5 + 445*x^6 +...
The log of the g.f. equals the series:
log(A(x)) = x/sqrt(1-4*x) + (x^2/2)/sqrt(1-8*x^2) + (x^3/3)/sqrt(1-16*x^3) + (x^4/4)/sqrt(1-32*x^4) + (x^5/5)/sqrt(1-64*x^5) +...
and may be expressed in terms of the central binomial coefficients (A000984).
Explicitly, the logarithm begins:
log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 89*x^4/4 + 351*x^5/5 + 1601*x^6/6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (x^m/m)/sqrt(1-2*(2*x)^m+x*O(x^n)))), n)}

Crossrefs

Cf. A184513 (log).

Sequence in context: A148989 A047117 A148990 * A148991 A148992 A148993

Adjacent sequences: A184509 A184510 A184511 * A184513 A184514 A184515

Keyword

nonn

Author

Paul D. Hanna, Mar 18 2011

Status

approved