A304397 - OEIS

%I #5 May 12 2018 07:27:39

%S 1,15,9240,42073400,746084307150,36924991021460826,

%T 4160715480354842294820,930665660288187073185443460,

%U 374501250148595690153122892776875,251774218429254711234735482839554308125,266963725952364568003002013640838639863625156,426348840739731769879201369387693893984897112621140,987611583043183483323383128203849669908583985607235622200

%N a(n) = A304395(n) / (n+1)^5.

%F a(n) = (n+1)^(5*n)/(n+1)! - Sum_{k=1..n} (n+1)^(5*k-5)/k! * (n-k+1)^5 * a(n-k) for n>0 with a(0)=1.

%o (PARI) /* A304395 formula: [x^n] exp( n^5*x ) * (1 - x*A(x)) = 0 */

%o {A304395(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(x*m^5 +x^2*O(x^m)) * (1 - x*Ser(A)) )[m+1] ); A[n+1]}

%o for(n=0, 25, print1( A304395(n)/(n+1)^5, ", "))

%Y Cf. A304395.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 12 2018