A243486 O.g.f.: exp( Integral Sum_{n>=1} (2*n-1)! * x^(n-1) / Product_{k=1..2*n-1} (1 - k*x) dx ).

1, 1, 4, 56, 1808, 106232, 9896612, 1340462108, 248849495342, 60665985936086, 18799855981319036, 7218637248203263916, 3364163526700490152184, 1870786124908364192990576, 1223751739268135893514592188, 930266933532473430610242752804, 813248080956872294046978463360859

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 56*x^3 + 1808*x^4 + 106232*x^5 + 9896612*x^6 +...
The logarithmic derivative equals the series:
A'(x)/A(x) = 1/(1-x) + 3!*x/((1-x)*(1-2*x)*(1-3*x)) + 5!*x^2/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)) + 7!*x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)) + 9!*x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) +...
Explicitly, the logarithm of the o.g.f. begins:
log(A(x)) = x + 7*x^2/2 + 157*x^3/3 + 6991*x^4/4 + 521341*x^5/5 + 58702687*x^6/6 + 9311131117*x^7/7 + 1979781769231*x^8/8 +...

Prog

(PARI) {a(n)=polcoeff(exp(intformal(sum(m=1, n+1, (2*m-1)!*x^(m-1)/prod(k=1, 2*m-1, 1-k*x+x*O(x^n))))), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A243468, A243509.

Sequence in context: A111849 A009159 A013055 * A322733 A012983 A012959

Adjacent sequences: A243483 A243484 A243485 * A243487 A243488 A243489

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2014

Status

approved