A368536 - OEIS

%I #10 Dec 29 2023 08:06:40

%S 0,1,14,192,2996,53955,1110786,25808160,668740808,19129643325,

%T 598902606310,20371538593296,748148581865532,29505258575474591,

%U 1243695052515891626,55800352470853933440,2655106829377875895056,133547801741230053460761

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

%F a(n) = [x^n] n*x/((1-x) * (1-n*x)^3).

%F a(n) = n * (n^n * (n^4-n^3-3*n^2+3*n+2) - 2)/(2 * (n-1)^3) for n > 1.

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

%Y Cf. A062806, A368537.

%Y Cf. A368526.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Dec 29 2023