A304396 a(n) = A304394(n) / (n+1)^4.

1, 7, 941, 597571, 1077304324, 4250548204220, 31362344061243731, 389533784331698799757, 7553909607396308839307729, 216153962578005976317428630031, 8734715288242477329577387114158361, 481264969283514820342197141086713669943, 35132745658635258962977017094392007388046256, 3317919567828983194629673950155604531470409170896

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = (n+1)^(4*n)/(n+1)! - Sum_{k=1..n} (n+1)^(4*k-4)/k! * (n-k+1)^4 * 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))^4 * a(k)/(n-k)!.

G.f. A(x) satisfies [x^n] exp(n^4*x) (1 - E^4(x*A(x))) = 0 for n > 0, where E is the Euler operator x*d/dx. (End)

Prog

(PARI) /* A304394 formula: [x^n] exp( n^4*x ) * (1 - x*A(x)) = 0 */
{A304394(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(x*m^4 +x^2*O(x^m)) * (1 - x*Ser(A)) )[m+1] ); A[n+1]}
for(n=0, 25, print1( A304394(n)/(n+1)^4, ", "))

Crossrefs

Cf. A107669, A304394, A304397.

Sequence in context: A038808 A068728 A028990 * A151579 A024098 A172918

Adjacent sequences: A304393 A304394 A304395 * A304397 A304398 A304399

Keyword

nonn

Author

Paul D. Hanna, May 12 2018

Status

approved