A287701 - OEIS

%I #12 Mar 02 2025 16:37:12

%S 0,1,2252,111753,1297504,7120505,25461756,70250257,163191008,

%T 335493009,629597260,1100904761,1819504512,2871901513,4362744764,

%U 6416555265,9179454016,12820890017,17535368268,23544177769,31097119520,40474234521,51987531772,65982716273,82840917024,102980415025,126858371276,154972554777

%N a(n) = (5!)^3 * [z^5] hypergeom([], [1,1], z)^n.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F O.g.f.: x*(1 + 2246*x + 98256*x^2 + 660746*x^3 + 966751*x^4) / (1 - x)^6.

%F a(n) = 163476*n - 375375*n^2 + 305500*n^3 - 108000*n^4 + 14400*n^5.

%F a(n) = [x^n] (x + 2246*x^2 + 98256*x^3 + 660746*x^4 + 966751*x^5) / (1 - x)^6.

%p a := n -> 163476*n - 375375*n^2 + 305500*n^3 - 108000*n^4 + 14400*n^5:

%p seq(a(n), n=0..27);

%t Table[163476 n - 375375 n^2 + 305500 n^3 - 108000 n^4 + 14400 n^5, {n, 0, 30}] (* _Bruno Berselli_, Jun 06 2017 *)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,2252,111753,1297504,7120505},30] (* _Harvey P. Dale_, Mar 02 2025 *)

%Y Column 5 of A287698.

%K nonn,easy,changed

%O 0,3

%A _Peter Luschny_, Jun 01 2017