A290430 - OEIS

A290430

Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j*(j+1)*(2*j+1)/6))^k.

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 6, 1, 0, 1, 0, 1, 6, 10, 4, 0, 2, 0, 0, 1, 7, 15, 10, 1, 3, 2, 0, 0, 1, 8, 21, 20, 5, 4, 6, 0, 0, 0, 1, 9, 28, 35, 15, 6, 12, 3, 0, 0, 0, 1, 10, 36, 56, 35, 12, 20, 12, 0, 0, 0, 0, 1, 11, 45, 84, 70, 28, 31, 30, 4, 0, 1, 0, 0, 1, 12, 55, 120, 126, 64, 49, 60, 20, 0, 3, 0, 0, 0

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OFFSET

0,8

COMMENTS

A(n,k) is the number of ways of writing n as a sum of k square pyramidal numbers (A000330).

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Index to sequences related to pyramidal numbers

FORMULA

G.f. of column k: (Sum_{j>=0} x^(j*(j+1)*(2*j+1)/6))^k.

EXAMPLE