A303172 Number of ordered ways of writing n as a sum of n square pyramidal numbers.

1, 1, 1, 1, 1, 6, 31, 106, 281, 631, 1306, 2806, 6931, 19306, 55070, 150816, 391161, 977501, 2426071, 6141865, 16000186, 42465571, 112950916, 297793651, 776866355, 2015237231, 5233754306, 13668689206, 35908153534, 94633042267, 249398115466, 656105299636, 1723150461561

Offset

0,6

Links

Table of n, a(n) for n=0..32.

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Index to sequences related to pyramidal numbers

Formula

a(n) = [x^n] (Sum_{k>=0} x^(k*(k+1)*(2*k+1)/6))^n.

a(n) = A290430(n,n).

Mathematica

Table[SeriesCoefficient[Sum[x^(k (k + 1) (2 k + 1)/6), {k, 0, n}]^n, {x, 0, n}], {n, 0, 32}]

Crossrefs

Main diagonal of A290430.

Cf. A000330, A066535, A279220, A287617, A303170.

Sequence in context: A112562 A244716 A024447 * A354552 A143568 A351935

Adjacent sequences: A303169 A303170 A303171 * A303173 A303174 A303175

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2018

Status

approved