A107669 a(n) = A107668(n)/(n+1)^2.

1, 1, 5, 51, 809, 17575, 486460, 16384260, 650574249, 29762953831, 1541719486081, 89201504309927, 5702038255950404, 399105271607867940, 30359621863987241460, 2494052823831234355340, 220067051126228849480649, 20758555089315706637319735, 2084677809051987555703999639

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

From Seiichi Manyama, Mar 24 2026: (Start)

1/(n+1)! = Sum_{k=0..n} ((k+1)/(n+1)^(k+1))^2 * a(k)/(n-k)!.

G.f. A(x) satisfies [x^n] exp(n^2*x) (1 - E^2(x*A(x))) = 0 for n > 0, where E is the Euler operator x*d/dx. (End)

Prog

(PARI) {a(n)=local(A); if(n==0, n+1, A=(n+1)*x+x*O(x^n); for(k=0, n, A+=polcoeff(A, k)*x^k*(n+1-prod(i=0, k, 1+(i-n-1)*x))); polcoeff(A, n)/(n+1)^2)}

Crossrefs

Cf. A107667, A107668, A107670, A304396, A304397.

Sequence in context: A377803 A095839 A234290 * A218675 A182316 A077392

Adjacent sequences: A107666 A107667 A107668 * A107670 A107671 A107672

Keyword

nonn

Author

Paul D. Hanna, Jun 07 2005

Status

approved