A303170 Number of ordered ways of writing n as a sum of n tetrahedral numbers.

1, 1, 1, 1, 5, 21, 61, 141, 309, 757, 2111, 6051, 16721, 44617, 118301, 318501, 871781, 2400741, 6596953, 18067329, 49460555, 135697395, 373271515, 1028451579, 2835353337, 7819016521, 21572619771, 59562583471, 164586609409, 455114644297, 1259191262441, 3485551053561

Offset

0,5

Links

Table of n, a(n) for n=0..31.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Formula

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

a(n) = A290429(n,n).

Mathematica

Table[SeriesCoefficient[Sum[x^(k (k + 1) (k + 2)/6), {k, 0, n}]^n, {x, 0, n}], {n, 0, 31}]

Crossrefs

Main diagonal of A290429.

Cf. A000292, A068980, A106337, A282582, A303172.

Sequence in context: A370839 A203233 A112561 * A287617 A354551 A143567

Adjacent sequences: A303167 A303168 A303169 * A303171 A303172 A303173

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2018

Status

approved