A368537 - OEIS

%I #8 Dec 29 2023 08:06:45

%S 0,1,18,309,5828,123230,2913126,76405854,2205340936,69523722855,

%T 2377899710410,87721897714891,3472488925101516,146833416409808492,

%U 6605726035373765678,315051237815279406540,15879038919798268666896,843348814519524716426685

%N a(n) = Sum_{k=1..n} binomial(k+2,3) * n^k.

%F a(n) = [x^n] n*x /((1-x) * (1-n*x)^4).

%F a(n) = n * (n^n * (n^6-7*n^4+5*n^3+12*n^2-11*n-6) + 6)/(6 * (n-1)^4) for n > 1.

%o (PARI) a(n) = sum(k=1, n, binomial(k+2, 3)*n^k);

%Y Cf. A062806, A368536.

%Y Cf. A368527.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Dec 29 2023