A300589 a(n) = A300617(n) / (n*(n+1)/2) for n>=1.

1, 1, 5, 55, 1025, 28638, 1117831, 58157100, 3895841625, 327054041995, 33660663702514, 4170641243258042, 612634528823952155, 105303950053511041900, 20943400410601239618360, 4772694556432364600596272, 1235587041134996933696367753, 360653856192923791041427500825, 117894515649092645422159124253775, 42901062533218086978322192560871705

Offset: 1

Author

Paul D. Hanna, Mar 10 2018

Keywords

• nonn

Comments

It is conjectured that this sequence consists entirely of integers.

O.g.f. G(x) of A300617 satisfies: [x^n] exp(n*G(x)) = n^2 * [x^(n-1)] exp(n*G(x)) for n>=1.

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A300617, A300616.

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