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A272103 Convolution of nonzero heptagonal numbers (A000566) with themselves.

%I A272103 #6 Feb 16 2025 08:33:33
%S A272103 1,14,85,320,910,2156,4494,8520,15015,24970,39611,60424,89180,127960,
%T A272103 179180,245616,330429,437190,569905,733040,931546,1170884,1457050,
%U A272103 1796600,2196675,2665026,3210039,3840760,4566920,5398960,6348056,7426144,8645945,10020990,11565645,13295136
%N A272103 Convolution of nonzero heptagonal numbers (A000566) with themselves.
%H A272103 OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A272103 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>
%H A272103 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1)
%F A272103 O.g.f.: (1 + 4*x)^2/(1 - x)^6.
%F A272103 E.g.f.: (24 + 312*x + 696*x^2 + 424*x^3 + 85*x^4 + 5*x^5)*exp(x)/24.
%F A272103 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A272103 a(n) = (n + 1)*(n + 2)*(n + 3)*(5*n^2 + 5*n + 4)/24.
%t A272103 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 85, 320, 910, 2156}, 36]
%t A272103 Table[(n + 1) (n + 2) (n + 3) ((5 n^2 + 5 n + 4)/24), {n, 0, 35}]
%Y A272103 Cf. A000566.
%Y A272103 Cf. similar sequences of the convolution of k-gonal numbers with themselves listed in A271662.
%K A272103 nonn,easy
%O A272103 0,2
%A A272103 _Ilya Gutkovskiy_, Apr 20 2016