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Search: id:A152534
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| A152534 |
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Triangle T(n,k) read by rows with q-e.g.f.: 1/Product_{k>0}(1-x^k/faq(k,q)). |
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2
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| 1, 2, 1, 3, 3, 3, 1, 5, 7, 11, 11, 8, 4, 1, 7, 13, 25, 36, 44, 42, 36, 24, 13, 5, 1, 11, 24, 54, 93, 142, 184, 215, 222, 208, 172, 126, 81, 44, 19, 6, 1, 15, 39, 98, 195, 344, 532, 753, 964, 1150, 1264, 1294, 1226, 1082, 880, 661, 451, 278, 151, 70, 26, 7, 1
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein, q-Exponential Function from MathWorld.
Eric Weisstein, q-Factorial from MathWorld.
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FORMULA
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Sum_{k=0..binomial(n,2)}T(n,k)*q^k = Sum_{pi} faq(n,q)/Product_{i=1..n} faq(i,q)^e(i), where pi runs over all nonnegative integer solutions to e(1)+2*e(2)+...+n*e(n) = n and faq(i,q) = Product_{j=1..i} (q^j-1)/(q-1), i = 1..n. Sum_{k=0..binomial(n,2)} T(n,k)*exp(2*Pi*I*k/n)) = 1.
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EXAMPLE
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1; 2,1; 3,3,3,1; 5,7,11,11,8,4,1; 7,13,25,36,44,42,36,24,13,5,1; ...
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CROSSREFS
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Cf. A005651(row sums), A000041(first column), A076276(second column), A152474.
Sequence in context: A124770 A099246 A039775 this_sequence A136018 A138022 A113278
Adjacent sequences: A152531 A152532 A152533 this_sequence A152535 A152536 A152537
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KEYWORD
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nonn,tabf
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.yu), Dec 06 2008
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