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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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=0..17.

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

Cf. A118804, A215529.

Sequence in context: A145083 A234303 A138213 * A290129 A205319 A209917

Adjacent sequences:  A193330 A193331 A193332 * A193334 A193335 A193336

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 23 2011

STATUS

approved

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Last modified January 20 10:33 EST 2022. Contains 350472 sequences. (Running on oeis4.)