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A323220 a(n) = n*(n + 5)*(n + 7)*(n + 10)/24 + 1.

%I A323220 #13 Jan 29 2019 04:31:42
%S A323220 1,23,64,131,232,376,573,834,1171,1597,2126,2773,3554,4486,5587,6876,
%T A323220 8373,10099,12076,14327,16876,19748,22969,26566,30567,35001,39898,
%U A323220 45289,51206,57682,64751,72448,80809,89871,99672,110251,121648,133904,147061,161162,176251
%N A323220 a(n) = n*(n + 5)*(n + 7)*(n + 10)/24 + 1.
%F A323220 a(n) = [x^n] (8*x^4 - 31*x^3 + 41*x^2 - 18*x - 1)/(x - 1)^5.
%F A323220 a(n) = n! [x^n] exp(x)*(x^4 + 28*x^3 + 228*x^2 + 528*x + 24)/24.
%F A323220 a(n) = (1/3)*((2*n + 17)*a(n-3) - (3*n + 25)*a(n-2) + (n + 15)*a(n-1)) for n >= 3.
%F A323220 a(n) = A323224(n, 5).
%p A323220 a := n -> (n^4 + 22*n^3 + 155*n^2 + 350*n + 24)/24:
%p A323220 seq(a(n), n=0..40);
%Y A323220 Cf. A323224 (column 5), A323233 (row 5), A323221 (first diff.), A034856 (second diff.).
%K A323220 nonn,easy
%O A323220 0,2
%A A323220 _Peter Luschny_, Jan 25 2019