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A193333
G.f.: 1 = Sum_{n>=0} a(n)*x^n / Product_{k=1..n+1} (1+k*x)^3.
3
1, 3, 21, 244, 4056, 88770, 2426553, 79893084, 3085719033, 137035475333, 6888543200172, 387050951446488, 24058512516152880, 1640162160152393778, 121746052707050425113, 9778208522585460239036, 845181303653928350311539, 78247854362736258482850285
OFFSET
0,2
COMMENTS
Compare to the g.f. for factorials: 1 = Sum_{n>=0} n!*x^n/Product_{k=1..n+1} (1+k*x).
EXAMPLE
1 = 1/(1+x)^3 + 3*x/((1+x)^3*(1+2*x)^3) + 21*x^2/((1+x)^3*(1+2*x)^3*(1+3*x)^3) + 244*x^3/((1+x)^3*(1+2*x)^3*(1+3*x)^3*(1+4*x)^3) +...
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k/prod(j=1, k+1, 1+j*x+x*O(x^n))^3), n))}
CROSSREFS
Sequence in context: A145083 A234303 A138213 * A290129 A365602 A371006
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 23 2011
STATUS
approved