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A303170 Number of ordered ways of writing n as a sum of n tetrahedral numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A245240 A203233 A112561 * A287617 A143567 A147375

Adjacent sequences:  A303167 A303168 A303169 * A303171 A303172 A303173

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 19 2018

STATUS

approved

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Last modified November 12 22:16 EST 2019. Contains 329079 sequences. (Running on oeis4.)