A304397 a(n) = A304395(n) / (n+1)^5.

1, 15, 9240, 42073400, 746084307150, 36924991021460826, 4160715480354842294820, 930665660288187073185443460, 374501250148595690153122892776875, 251774218429254711234735482839554308125, 266963725952364568003002013640838639863625156, 426348840739731769879201369387693893984897112621140, 987611583043183483323383128203849669908583985607235622200

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

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.

From Seiichi Manyama, Mar 24 2026: (Start)

1/(n+1)! = Sum_{k=0..n} ((k+1)/(n+1)^(k+1))^5 * a(k)/(n-k)!.

G.f. A(x) satisfies [x^n] exp(n^5*x) (1 - E^5(x*A(x))) = 0 for n > 0, where E is the Euler operator x*d/dx. (End)

Prog

(PARI) /* A304395 formula: [x^n] exp( n^5*x ) * (1 - x*A(x)) = 0 */
{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]}
for(n=0, 25, print1( A304395(n)/(n+1)^5, ", "))

Crossrefs

Cf. A107669, A304395, A304396.

Sequence in context: A249967 A308156 A396054 * A206593 A200794 A230173

Adjacent sequences: A304394 A304395 A304396 * A304398 A304399 A304400

Keyword

nonn

Author

Paul D. Hanna, May 12 2018

Status

approved