A185054 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n*(1-x)^n / Product_{k=1..n-1} (1 + k*x).

1, 1, 2, 7, 35, 226, 1780, 16489, 175191, 2095995, 27844858, 406243180, 6451271440, 110696475526, 2039751769020, 40151423775525, 840515332739587, 18638310752208047, 436301221978291734, 10748794565787775575, 277935932581614865791, 7524554625329583923280

Offset

0,3

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n! * x^n/Product_{k=1..n} (1 + k*x).

Links

Table of n, a(n) for n=0..21.

Example

 G.f.: 1/(1-x) = 1 + 1*x*(1-x) + 2*x^2*(1-x)^2/(1+x) + 7*x^3*(1-x)^3/((1+x)*(1+2*x)) + 35*x^4*(1-x)^4/((1+x)*(1+2*x)*(1+3*x)) + 226*x^5*(1-x)^5/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) +...

Prog

 (PARI) {a(n)=if(n<0, 0, 1-polcoeff(sum(k=0, n-1, a(k)*x^k*(1-x)^k/prod(j=0, k-1, 1+j*x+x*O(x^n))), n))}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A132624.

Sequence in context: A182224 A317421 A292182 * A014307 A000154 A003713

Adjacent sequences: A185051 A185052 A185053 * A185055 A185056 A185057

Keyword

nonn

Author

Paul D. Hanna, Mar 02 2012

Status

approved