A397243 L.g.f. Sum_{n>=1} a(n)*x^n/n = log(1+x + Sum_{n>=2} n/(n^2-1) * a(n)*x^n ).

1, 3, 40, 915, 30816, 1413930, 84513360, 6384139587, 595609853440, 67353819584238, 9087133029153840, 1442929646432008878, 266495181531171493824, 56660732059178616326100, 13743303287006807329982880, 3772610857852397449962995235, 1163717696949502364569525508352, 400819880895705955239599615666790

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..500

Formula

Forms the logarithmic derivative of the g.f. of A397242.

a(n) = (n^2-1)/n * A397242(n) for n > 1 with a(1) = 1.

Example

L.g.f.: L(x) = x + 3*x^2/2 + 40*x^3/3 + 915*x^4/4 + 30816*x^5/5 + 1413930*x^6/6 + 84513360*x^7/7 + 6384139587*x^8/8 + ...
where
exp(L(x)) = 1 + x + 2*x^2 + 15*x^3 + 244*x^4 + 6420*x^5 + 242388*x^6 + 12324865*x^7 + ... + n/(n^2-1) * a(n)*x^n + ...

Prog

(PARI) {a(n) = my(L=[0, 1], A, m); for(i=2, n, L=concat(L, 0); A = exp(Ser(L)); m = #L-1;
L[#L] = (m^2-1)*polcoef(A, m) - m^2*polcoef(log(A), m) ); GF=Ser(L); L[n+1]}
\\ returns a vector of terms a(k) for k = 1..n
{upto(n) = a(n); Vec(GF')}
upto(25)

Crossrefs

Cf. A397241, A397242.

Sequence in context: A143640 A341849 A358368 * A260754 A047799 A204515

Adjacent sequences: A397240 A397241 A397242 * A397244 A397245 A397247

Keyword

nonn

Author

Paul D. Hanna, Jun 19 2026

Status

approved