|
| |
|
|
A132684
|
|
a(n) = C(2^n + n + 1, n).
|
|
3
| |
|
|
1, 4, 21, 220, 5985, 501942, 143218999, 145944307080, 542150225230185, 7398714129087308170, 372134605932348010322571, 69146263065062394421802892300, 47589861944854471977019273909187085
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
FORMULA
| a(n) = [x^n] 1/(1-x)^(2^n + 2).
G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)^2*n!). [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
|
|
|
EXAMPLE
| Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009: (Start)
G.f.: A(x) = 1 + 4*x + 21*x^2 + 220*x^3 + 5985*x^4 + 501942*x^5 +...
A(x) = 1/(1-x)^2 - log(1-2x)/(1-2x)^2 + log(1-4x)^2/((1-4x)^2*2!) - log(1-8x)^3/((1-8x)^2*3!) +-... (End)
|
|
|
MATHEMATICA
| Table[Binomial[2^n+n+1, n], {n, 0, 20}] (* From Harvey P. Dale, Nov 10 2011 *)
|
|
|
PROG
| (PARI) a(n)=binomial(2^n+n+1, n)
(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))^2*m!)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
|
|
|
CROSSREFS
| Cf. A060690, A132683.
Cf. A066384. [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
Sequence in context: A158258 A065527 A041667 * A032074 A197662 A203218
Adjacent sequences: A132681 A132682 A132683 * A132685 A132686 A132687
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 26 2007
|
| |
|
|
