A300872 a(n) = A300871(n) / (n*(n+1)/2).

1, 1, 8, 151, 4752, 214848, 12915744, 986580860, 92994888960, 10595684332288, 1436363905680384, 228679178713630208, 42284602089642237952, 8992606241049735405568, 2180532527491138011131904, 598191016068264518151780096, 184370870332464252513762869248, 63445183762362816656030378164224, 24238363163428954774170892697075712

Offset: 1

Author

Paul D. Hanna, Mar 14 2018

Keywords

• nonn

Comments

It is conjectured that this sequence consists entirely of integers.

O.g.f. G(x) of A300871 satisfies: [x^n] exp( n*(n+1) * G(x) ) = n*(n+1) * [x^(n-1)] exp( n*(n+1) * G(x) ) for n>=1.

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A300871.

Programs

PARI

{a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)*(#A))); A[#A] = ((#A-1)*(#A)*V[#A-1] - V[#A])/(#A-1)/(#A) ); (1/(n*(n+1)/2))*polcoeff( log(Ser(A)), n)}
for(n=1, 20, print1(a(n), ", "))