A199882 E.g.f. A(x) satisfies differential equation A'''(x)=A(x)+A(x)^2, A(0)=0, A'(0)=1, A''(0)=1, A'''(0)=1.

1, 1, 1, 1, 3, 7, 15, 33, 93, 309, 1071, 3699, 13947, 58293, 260337, 1202121, 5797035, 29682639, 161252631, 915546969, 5401610901, 33227826669, 213648580503, 1430820925083, 9936454523427

Offset

1,5

Links

Table of n, a(n) for n=1..25.

Formula

a(n)=n!*b(n), b(n)=1/(n*(n-1)*(n-2))*(i=1..n-4, b(n-3)+sum(b(i)*b(n-3-i))), n>3, b(1)=1, b(2)=1/2, b(3)=1/6.

Prog

(Maxima)
a(n):=if n<4 then 1/n! else 1/(n*(n-1)*(n-2))*(a(n-3)+sum(a(i)*a(n-3-i), i, 1, n-4));
makelist(n!*a3(n), n, 1, 25);

Crossrefs

Sequence in context: A101892 A211279 A351660 * A147102 A147379 A213722

Adjacent sequences: A199879 A199880 A199881 * A199883 A199884 A199885

Keyword

nonn

Author

Vladimir Kruchinin, Nov 18 2011

Status

approved