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A078124 Second column, M(n+1,1) for n>=0, of infinite lower triangular matrix M defined in A078122. 17
1, 3, 12, 93, 1632, 68457, 7112055, 1879090014, 1287814075131, 2325758241901161, 11213788533232011006, 145939965725683888932081, 5174322925070232320838406581, 503750821963423009552527526376232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..40

FORMULA

The partitions of 2*3^n into powers of 3, or, the coefficient of x^(2*3^n) in 1/Product_{j=0..inf}(1-x^(3^j)) (conjecture).

EXAMPLE

a(1)=3 since the coefficient of x^6 in 1/Product_{j=0..inf}(1-x^(3^j)) = 1 + x + x^2 + 2x^3 + 2x^4 + 2x^5 + 3x^6 + ... is 3.

MATHEMATICA

m[i_, j_] := m[i, j]=If[j==0||i==j, 1, m3[i-1, j-1]]; m2[i_, j_] := m2[i, j]=Sum[m[i, k]m[k, j], {k, j, i}]; m3[i_, j_] := m3[i, j]=Sum[m[i, k]m2[k, j], {k, j, i}]; a[n_] := m[n+1, 1]

CROSSREFS

Cf. A078121, A078122 (matrix shift when cubed), A078123, A078125.

Sequence in context: A058337 A025503 A263801 * A115245 A145074 A162055

Adjacent sequences:  A078121 A078122 A078123 * A078125 A078126 A078127

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 18 2002

STATUS

approved

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Last modified May 25 21:46 EDT 2020. Contains 334597 sequences. (Running on oeis4.)