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A082579
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A binomial sum.
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1
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1, 1, 5, 31, 241, 2261, 24781, 309835, 4342241, 67308841, 1141960501, 21026890391, 417264626065, 8871853115581, 201100863674621, 4838817223845571, 123128720142540481, 3302478863343928145, 93091427773284348901
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = n!*sum(k=1..n, binomial(n+k-1,2*k-1)/k!).
Recurrence: a(n+3) - (3*n+7)*a(n+2) + (n+2)*(3*n+2)*a(n+1) - (n+2)*(n+1)*n*a(n) = 0.
E.g.f.: exp( x/( 1 - x )^2 ).
Special values of the hypergeometric function 2F2 : a(n)=n!*n*hypergeom([n+1, -n+1], [3/2, 2], -1/4), n>=1. From Karol A. Penson - (penson(AT)lptl.jussieu.fr)- Jan 29 04.
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PROG
| (Maxima)
a(n):=n!*sum(binomial(n+k-1, 2*k-1)/k!, k, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 21 2011]
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CROSSREFS
| Sequence in context: A069321 A177797 A186859 * A024451 A046852 A056541
Adjacent sequences: A082576 A082577 A082578 * A082580 A082581 A082582
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KEYWORD
| easy,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), May 07 2003
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