A226838 E.g.f.: exp( Sum_{n>=1} x^(n^2) / n^n ).

1, 1, 1, 1, 7, 31, 91, 211, 1681, 25537, 192361, 949081, 4830871, 85109311, 951416467, 6696998491, 119863554721, 2004272484481, 25344895874641, 237953743909297, 4116426696101671, 65285723209356511, 903886886890585291, 10132514132979331171, 165368713321379497777, 9835535504812487849281

Offset

0,5

Comments

E.g.f. may be written as: exp( Sum_{n>=1} ( x^n/n )^n ).

Sum_{n>=0} a(n)/n! = exp( Sum_{n>=1} 1/n^n ) = 3.63746131381110156231...

Links

Table of n, a(n) for n=0..25.

Formula

a(n) == 1 (mod 6) (conjecture - valid up to n=1024; if true for n>=0, why?).

Example

E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 7*x^4/4! + 31*x^5/5! + 91*x^6/6! +...
where
log(A(x)) = x + x^4/2^2 + x^9/3^3 + x^16/4^4 + x^25/5^5 + x^36/6^6 + x^49/7^7 +...

Prog

(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, (x^m/m)^m)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A226839, A226890.

Sequence in context: A262012 A118934 A118935 * A205801 A193437 A199921

Adjacent sequences: A226835 A226836 A226837 * A226839 A226840 A226841

Keyword

nonn

Author

Paul D. Hanna, Jun 19 2013

Status

approved