A243509 O.g.f.: exp( Integral Sum_{n>=1} (2*n)! * x^(n-1) / Product_{k=1..2*n} (1 - k*x) dx ).

1, 2, 17, 356, 15050, 1090340, 120880118, 19006269152, 4019815232183, 1100169446737862, 378260919290968391, 159596027891781179588, 81074448438738151958144, 48811678984945504941033320, 34368839633409849003075848348, 27981522156103308265337853752864

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Example

G.f.: A(x) = 1 + 2*x + 17*x^2 + 356*x^3 + 15050*x^4 + 1090340*x^5 +...
The logarithmic derivative equals the series:
A'(x)/A(x) = 2!/((1-x)*(1-2*x)) + 4!*x/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + 6!*x^2/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)) + 8!*x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)*(1-7*x)*(1-8*x)) + 10!*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)*(1-10*x)) +...
Explicitly, the logarithm of the o.g.f. begins:
log(A(x)) = 2*x + 30*x^2/2 + 974*x^3/3 + 57030*x^4/4 + 5280302*x^5/5 + 710771670*x^6/6 + 131223143774*x^7/7 +...

Prog

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

Crossrefs

Cf. A243486.

Sequence in context: A378044 A373324 A330260 * A128159 A319591 A198405

Adjacent sequences: A243506 A243507 A243508 * A243510 A243511 A243512

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2014

Status

approved