A243468 O.g.f.: exp( Integral Sum_{n>=1} (2*n-1)!/(n-1)! * x^(n-1) / Product_{k=1..n} (1 - (2*k-1)*x) dx ).

1, 1, 4, 32, 401, 6941, 154092, 4181124, 134128092, 4966119716, 208417559828, 9776282249324, 506839013285272, 28777453303699456, 1775899632802691548, 118352734502149514340, 8471167817556712646853, 648104081945726392459965, 52780511829697565513665400

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 32*x^3 + 401*x^4 + 6941*x^5 + 154092*x^6 +...
The logarithmic derivative equals the series:
A'(x)/A(x) = 1/(1-x) + 3!*x/((1-x)*(1-3*x)) + 5!/2!*x^2/((1-x)*(1-3*x)*(1-5*x)) + 7!/3!*x^3/((1-x)*(1-3*x)*(1-5*x)*(1-7*x)) + 9!/4!*x^4/((1-x)*(1-3*x)*(1-5*x)*(1-7*x)*(1-9*x)) +...
Explicitly, the logarithm of the o.g.f. begins:
log(A(x)) = x + 7*x^2/2 + 85*x^3/3 + 1459*x^4/4 + 32281*x^5/5 + 873967*x^6/6 + 27981325*x^7/7 + 1034079739*x^8/8 +...

Prog

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

Crossrefs

Cf. A243486.

Sequence in context: A195762 A127670 A317403 * A317677 A365603 A191459

Adjacent sequences: A243465 A243466 A243467 * A243469 A243470 A243471

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2014

Status

approved