|
|
A156213
|
|
G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*C(2*n-1,n)*x^n/n ), a power series in x with integer coefficients.
|
|
1
|
|
|
1, 2, 26, 1756, 577190, 846763548, 5293107304932, 138013765804872888, 14838375909837963204230, 6530915607537754235471687212, 11710315776946229385945240614099084
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Compare to g.f. of Catalan sequence: exp( Sum_{n>=1} C(2*n-1,n)*x^n/n ), where C(2*n-1,n) = A001700(n-1).
|
|
LINKS
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 + 2*x + 26*x^2 + 1756*x^3 + 577190*x^4 + 846763548*x^5 +...
log(A(x)) = 2*x + 2^4*3*x^2/2 + 2^9*10*x^3/3 + 2^16*35*x^4/4 + 2^25*126*x^5/5 +...
|
|
PROG
|
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 2^(m^2)*binomial(2*m-1, m)*x^m/m)+x*O(x^n)), n)}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|