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
Keywords
Links
- Eric Weisstein's World of Mathematics, Square Pyramidal Number
- Index to sequences related to pyramidal numbers
Programs
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Mathematica
Table[SeriesCoefficient[Sum[x^(k (k + 1) (2 k + 1)/6), {k, 0, n}]^n, {x, 0, n}], {n, 0, 32}]
Formula
a(n) = [x^n] (Sum_{k>=0} x^(k*(k+1)*(2*k+1)/6))^n.
a(n) = A290430(n,n).