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A126462
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Column 2 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.
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4
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1, 1, 6, 75, 1565, 48950, 2145626, 125727238, 9507150815, 902519025315, 105203477607220, 14786330708536422, 2467862211341410635, 482812610434512386665, 109492763990117261581870
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 9*k + 20)*k/6].
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EXAMPLE
| Equals the number of subpartitions of the partition:
{(k^2 + 9*k + 20)*k/6, k>=0} = [0,5,14,28,48,75,110,154,208,273,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^5 + 6*x^2*(1-x)^14 + 75*x^3*(1-x)^28 + 1565*x^4*(1-x)^48 + 48950*x^5*(1-x)^75 + 2145626*x^6*(1-x)^110 + 125727238*x^7*(1-x)^154 ...
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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+9*k+20)*k/6)), n)}
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CROSSREFS
| Cf. A126460; A126461, A126463, A126464.
Sequence in context: A139088 A193784 A162863 * A081066 A185289 A016090
Adjacent sequences: A126459 A126460 A126461 * A126463 A126464 A126465
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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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