A395121 a(n) = A395120(n+1)/(n+1) for n >= 0.

1, 1, 3, 16, 137, 1746, 30787, 708289, 20393697, 713704924, 29707484531, 1446005259579, 81182236620817, 5197625956902718, 375890959014970323, 30458434507868797231, 2745996328319300018913, 273765648582428330478776, 30018774941547810310868707, 3602830336301261670977620531

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 137*x^4/4! + 1746*x^5/5! + 30787*x^6/6! + 708289*x^7/7! + 20393697*x^8/8! + ...
Let B(x) = x*A(x) then
A(x) = 1 + B(x) + x*B(B(x))/2! + x^2*B(B(B(x)))/3! + x^3*B(B(B(B(x))))/4! + ... + x^(n-1)*B^n(x)/n! + ....
where
B(x) = x + 2*x^2/2! + 9*x^3/3! + 64*x^4/4! + 685*x^5/5! + 10476*x^6/6! + ... + A395120(n)*x^n/n! + ...
satisfies B(x) = Sum_{n>=0} B^n(x) * x^n/n!.

Prog

(PARI) \\ Routine to calculate the n-th iteration
{IT(n, F) = my(G=x); for(i=1, n, G = subst(F, x, G)); G}
\\ Get e.g.f. from iterations of B(x) (e.g.f. of A395120)
{a(n) = my(B=x); for(k=1, n, B = truncate(B) + x*O(x^k);
B = sum(m=0, k, x^m/m! * IT(m, B) ) ); polcoef(EGF=B/x, n)}
{upto(n) = a(n); Vec(serlaplace(EGF))}
upto(20)

Crossrefs

Cf. A395120.

Sequence in context: A368293 A386642 A345349 * A230320 A230318 A006057

Adjacent sequences: A395118 A395119 A395120 * A395122 A395123 A395124

Keyword

nonn

Author

Paul D. Hanna, May 10 2026

Status

approved