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A126462 Column 2 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}. 4

%I

%S 1,1,6,75,1565,48950,2145626,125727238,9507150815,902519025315,

%T 105203477607220,14786330708536422,2467862211341410635,

%U 482812610434512386665,109492763990117261581870

%N Column 2 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.

%F G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 9*k + 20)*k/6].

%e Equals the number of subpartitions of the partition:

%e {(k^2 + 9*k + 20)*k/6, k>=0} = [0,5,14,28,48,75,110,154,208,273,...]

%e as illustrated by g.f.:

%e 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 ...

%o (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)}

%Y Cf. A126460; A126461, A126463, A126464.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 27 2006

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Last modified January 19 15:13 EST 2022. Contains 350466 sequences. (Running on oeis4.)