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Search: id:A126348
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| 1, 1, 2, 4, 7, 12, 20, 33, 53, 84, 131, 202, 308, 465, 695, 1030, 1514, 2209, 3201, 4609, 6596, 9386, 13284, 18705, 26211, 36561, 50776, 70226, 96742, 132765, 181540, 247369, 335940, 454756, 613689, 825698, 1107755, 1482038, 1977465, 2631664
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OFFSET
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0,3
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COMMENT
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In triangle A126347, row n lists coefficients of q in B(n,q) that satisfies: B(n,q) = Sum_{k=0..n-1} C(n-1,k)*B(k,q)*q^k for n>0, with B(0,q) = 1; row sums equal the Bell numbers: B(n,1) = A000110(n).
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FORMULA
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1 + Sum_{k>0} x^(k * (k + 1) / 2) / ((1 - x)^k * (1 - x) * (1 - x^2) ... (1 - x^k)). - Michael Somos Aug 17 2008
G.f.: Product_{k>0} (1+x^k/(1-x)). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Oct 05 2008]
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PROGRAM
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(PARI) {B(n, q)=if(n==0, 1, sum(k=0, n-1, binomial(n-1, k)*B(k, q)*q^k))} {a(n)=Vec(B(n+1, q)+O(q^(n*(n-1)/2+1)))[n*(n-1)/2+1]}
(PARI) {a(n) = local(t); if( n<0, 0, t = 1; polcoeff( sum(k=1, (sqrtint(8*n + 1) - 1)\2, t = t * x^k / (1 - x) / (1 - x^k) + x * O(x^n), 1), n))} /* Michael Somos Aug 17 2008 */
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CROSSREFS
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Cf. A126347, A126349; factorial variant: A126471.
Sequence in context: A101230 A128129 A014968 this_sequence A006731 A000071 A093607
Adjacent sequences: A126345 A126346 A126347 this_sequence A126349 A126350 A126351
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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), Dec 31 2006
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