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Search: id:A127728
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| A127728 |
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Sum of squared coefficients of q in the q-factorials. |
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+0
5
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| 1, 1, 2, 10, 106, 1930, 53612, 2108560, 111482424, 7625997280, 655331699940, 69110082376388, 8775534280695310, 1320693932817784342, 232459627389638257316, 47311901973588298051380
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, q-Factorial from MathWorld.
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EXAMPLE
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Definition of q-factorial of n:
faq(n) = Product_{k=1..n} (1-q^k)/(1-q) for n>0, with faq(0)=1;
faq(4) = 1*(1 + q)*(1 + q + q^2)*(1 + q + q^2 + q^3) = 1 + 3*q + 5*q^2 + 6*q^3 + 5*q^4 + 3*q^5 + q^6;
then a(n) is the sum of squared coefficients of q:
a(4) = 1^2 + 3^2 + 5^2 + 6^2 + 5^2 + 3^2 + 1^2 = 106.
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PROGRAM
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(PARI) {a(n)=local(faq_n=if(n==0, 1, prod(k=1, n, (1-q^k)/(1-q)))); sum(k=0, n*(n-1)/2, polcoeff(faq_n, k, q)^2)}
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CROSSREFS
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Sequence in context: A000595 A087234 A049538 this_sequence A003222 A003167 A062412
Adjacent sequences: A127725 A127726 A127727 this_sequence A127729 A127730 A127731
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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), Jan 25 2007
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