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A303172 Number of ordered ways of writing n as a sum of n square pyramidal numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A143568 A166786 A003728

Adjacent sequences:  A303169 A303170 A303171 * A303173 A303174 A303175

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 19 2018

STATUS

approved

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Last modified February 22 11:41 EST 2020. Contains 332135 sequences. (Running on oeis4.)