A336303 - OEIS

%I #7 Oct 04 2020 08:47:36

%S 1,1,0,0,6,0,180,630,1120,36288,441000,6579870,59734620,1252872192,

%T 13668490836,162131872695,2971275208720,52783774330940,

%U 1334562954639156,16933262255752698,406499325562503480,8838644883526856832,190698441426122689290

%N Number of ordered ways of writing the n-th n-gonal pyramidal number as a sum of n nonzero n-gonal pyramidal numbers.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%F a(n) = [x^p(n,n)] (Sum_{k=1..n} x^p(n,k))^n, where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.

%e a(4) = 6 because the fourth square pyramidal number is 30 and we have [14, 14, 1, 1], [14, 1, 14, 1], [14, 1, 1, 14], [1, 14, 14, 1], [1, 14, 1, 14] and [1, 1, 14, 14].

%t Join[{1},Table[SeriesCoefficient[Sum[x^(k (k + 1) (k (n - 2) - n + 5)/6), {k, 1, n}]^n, {x, 0, n (n + 1) (n^2 - 3 n + 5)/6}], {n, 1, 22}]]

%Y Cf. A006484, A298858, A335634, A336091, A337797, A337798, A337799.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Oct 04 2020