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A376778 a(n) = (32*n^4 + 80*n^3 + 40*n^2 - 20*n + 3)*(2*n + 1)*n/15.

%I A376778 #19 Jul 09 2025 05:07:08
%S A376778 0,27,850,7077,33300,113311,312390,742665,1581544,3093219,5653242,
%T A376778 9776173,16146300,25651431,39419758,58859793,85703376,122051755,
%U A376778 170424738,233812917,315732964,420285999,552219030,716989465,920832696,1170832755,1474996042,1842328125,2282913612,2807999095,3430079166,4162985505,5021979040,6023845179,7186992114,8531552197,10079486388
%N A376778 a(n) = (32*n^4 + 80*n^3 + 40*n^2 - 20*n + 3)*(2*n + 1)*n/15.
%H A376778 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A376778 From _Stefano Spezia_, Nov 12 2024: (Start)
%F A376778 G.f.: x*(27 + 661*x + 1694*x^2 + 666*x^3 + 23*x^4 + x^5)/(1 - x)^7.
%F A376778 E.g.f.: exp(x)*x*(405 + 5970*x + 11520*x^2 + 6240*x^3 + 1152*x^4 + 64*x^5)/15. (End)
%o A376778 (Python)
%o A376778 def A376778(n): return n*(n*(n**2*(n*(n+3<<6)+160)-14)+3)//15 # _Chai Wah Wu_, Nov 11 2024
%Y A376778 Cf. A376777, A014105, A377858.
%K A376778 nonn,easy
%O A376778 0,2
%A A376778 _N. J. A. Sloane_, Nov 10 2024, following a suggestion from _Fredrik Johansson_ (see A376777)