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A126461 Column 0 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 3*k - 4)*k/6, k>=0}. 4
1, 1, 1, 3, 21, 274, 5806, 182766, 8034916, 471517614, 35682799508, 3388864405941, 395127873991296, 55543575452873070, 9271180003481197642, 1813921568747948684475, 411378931233397975750296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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}.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 3*k - 4)*k/6].

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 ...

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)}

CROSSREFS

Cf. A126460; A126462, A126463, A126464.

Sequence in context: A066206 A130032 A174967 * A000681 A222035 A171201

Adjacent sequences:  A126458 A126459 A126460 * A126462 A126463 A126464

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 27 2006

STATUS

approved

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Last modified January 16 22:12 EST 2022. Contains 350376 sequences. (Running on oeis4.)