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A201007
G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n / Product_{k=1..n} (1 + n*k*x).
0
1, 1, 2, 12, 162, 4020, 161190, 9580200, 794045490, 87732586200, 12482467492950, 2225389826721600, 486286707998356650, 127896148968309802080, 39873063650831725704390, 14545617596016448962820800, 6140116931023810866657175650, 2970359726329509983655533867520
OFFSET
0,3
COMMENTS
Compare to a g.f. involving the factorial numbers:
1/(1-x) = Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 + k*x).
Also compare to a g.f. of A220181:
Sum_{n>=0} n^n * n! * x^n / Product_{k=1..n} (1 + n*k*x).
EXAMPLE
1/(1-x) = 1 + x/(1+x) + 2*x^2/((1+2*1*x)*(1+2*2*x)) + 12*x^3/((1+3*1*x)*(1+3*2*x)*(1+3*3*x)) + 162*x^4/((1+4*1*x)*(1+4*2*x)*(1+4*3*x)*(1+4*4*x)) + 4020*x^5/((1+5*1*x)*(1+5*2*x)*(1+5*3*x)*(1+5*4*x)*(1+5*5*x)) +...
PROG
(PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, k, 1+k*j*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A180420 A012328 A302688 * A226058 A120958 A030163
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 08 2013
STATUS
approved