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Number of compositions (ordered partitions) of n into heptagonal pyramidal numbers (A002413).
3

%I #5 Dec 29 2018 14:32:58

%S 1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,11,14,18,23,29,36,44,53,64,78,97,121,

%T 151,188,233,287,352,431,530,654,809,1002,1241,1535,1895,2335,2876,

%U 3544,4371,5396,6666,8237,10176,12564,15504,19126,23594,29111,35928

%N Number of compositions (ordered partitions) of n into heptagonal pyramidal numbers (A002413).

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

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(5*k-2)/6)).

%t nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (5 k - 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A002413, A279223, A282582, A322340, A322799, A322803, A322853, A322854, A322856.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Dec 29 2018