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A208831 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..2*n} (1 + k*x). 1
1, 1, 4, 34, 470, 9246, 239254, 7735818, 301515326, 13798284326, 726653380406, 43347208596090, 2892081998352630, 213573932091190350, 17305963353368021974, 1527409032389494461130, 145910774659458343922094, 15004445714376212721001782, 1653029709428208769065420054 (list; graph; refs; listen; history; text; internal format)
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..18.

EXAMPLE

G.f.: 1/(1-x) = 1 + 1*x/((1+x)*(1+2*x)) + 4*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) + 34*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)) + 470*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)) +...

PROG

(PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, 2*k, (1+j*x+x*O(x^n)) )), n))}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A208830.

Sequence in context: A321264 A234291 A193099 * A294475 A198976 A156325

Adjacent sequences:  A208828 A208829 A208830 * A208832 A208833 A208834

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 01 2012

STATUS

approved

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Last modified May 24 18:12 EDT 2022. Contains 354043 sequences. (Running on oeis4.)