A362733 a(n) = [x^n] F(x)^n, where F(x) = exp( Sum_{k >= 1} A362732(k)*x^k/k ).

1, 6, 234, 10428, 492522, 24033006, 1197423396, 60530725380, 3092592004074, 159295600885794, 8258018380659234, 430335300869496072, 22521831447746893092, 1182951246247357578348, 62325193477833011143260, 3292376206935392483917428, 174323297281680647978503146, 9248680725006429075147528150

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n*p^r) == a(n*p^(r-1)) (mod p^r) (Gauss congruence) holds for all primes p and positive integers n and r.

Conjecture: the supercongruence a(n*p^r) == a(n*p^(r-1)) (mod p^(3*r)) holds for all primes p >= 3 and positive integers n and r.

Maple

E(n, x) := series(exp(n*add((3*k)!/k!^3*x^k/k, k = 1..20)), x, 21):
A362732(n) := coeftayl(E(n, x), x = 0, n):
F(n, x) := series(exp(n*add(A362732(k)*x^k/k, k = 1..20)), x, 21):
seq(coeftayl(F(n, x), x = 0, n), n = 0..20);

Crossrefs

Cf. A006480, A362722 - A362732.

Sequence in context: A307888 A194482 A309330 * A266657 A145180 A256275

Adjacent sequences: A362730 A362731 A362732 * A362734 A362735 A362736

Keyword

nonn,easy

Author

Peter Bala, May 06 2023

Status

approved