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Search: id:A129256
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| A129256 |
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Central coefficient of Product_{k=0..n} (1+k*x)^2. |
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+0
1
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| 1, 2, 13, 144, 2273, 46710, 1184153, 35733376, 1251320145, 49893169050, 2232012515445, 110722046632560, 6032418472347265, 358103844593876654, 23007314730623658225, 1590611390957425536000, 117745011140615270168865
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = (-1)^n*Sum_{k=0..n} Stirling1(n+1,k+1)*Stirling1(n+1,n-k+1). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 16 2009]
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EXAMPLE
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This sequence equals the central terms of the triangle in which the g.f. of row n is (1+x)^2*(1+2x)^2*(1+3x)^2*...*(1+n*x)^2, as illustrated by:
(1);
1,(2),1;
1,6,(13),12,4;
1,12,58,(144),193,132,36;
1,20,170,800,(2273),3980,4180,2400,576;
1,30,395,3000,14523,(46710),100805,143700,129076,65760,14400; ...
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PROGRAM
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(PARI) a(n)=polcoeff(prod(k=0, n, 1+k*x)^2, n)
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Jul 16 2009: (Start)
(PARI) {Stirling1(n, k)=if(n==0, 1, n!*polcoeff(binomial(x, n), k))}
{a(n)=(-1)^n*sum(k=0, n, Stirling1(n+1, k+1)*Stirling1(n+1, n-k+1))} (End)
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CROSSREFS
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Cf. A008275 (Stirling1 numbers).
Cf. A008275 (Stirling1). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 16 2009]
Sequence in context: A003414 A003326 A003581 this_sequence A046245 A107699 A079330
Adjacent sequences: A129253 A129254 A129255 this_sequence A129257 A129258 A129259
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 06 2007
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