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A126461
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Column 0 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 3*k - 4)*k/6, k>=0}.
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4
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1, 1, 1, 3, 21, 274, 5806, 182766, 8034916, 471517614, 35682799508, 3388864405941, 395127873991296, 55543575452873070, 9271180003481197642, 1813921568747948684475, 411378931233397975750296
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| When shifted left, equals column 1 of triangle A126460, which is the number of subpartitions of partition: {(k^2 + 6*k + 5)*k/6, k>=0}.
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FORMULA
| G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 3*k - 4)*k/6].
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EXAMPLE
| Equals the number of subpartitions of the partition:
{(k^2 + 3*k - 4)*k/6, k>=0} = [0,0,2,7,16,30,50,77,112,156,210,275,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^0 + 1*x^2*(1-x)^2 + 3*x^3*(1-x)^7 + 21*x^4*(1-x)^16 + 274*x^5*(1-x)^30 + 5806*x^6*(1-x)^50 + 182766*x^7*(1-x)^77 ...
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PROG
| (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+3*k-4)*k/6)), n)}
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CROSSREFS
| Cf. A126460; A126462, A126463, A126464.
Sequence in context: A098278 A066206 A130032 * A000681 A171201 A193206
Adjacent sequences: A126458 A126459 A126460 * A126462 A126463 A126464
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2006
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