A259112 E.g.f. satisfies: A(x) = Integral 1 + A(x)^7 dx.

1, 5040, 76281004800, 37626350120206848000, 185657801986983855655526400000, 5150422429203073500358041285476352000000, 569512147150397429576160463881863910421954560000000, 199607288101583292042564550150623446229209414764068864000000000

Offset: 0

Author

Vaclav Kotesovec, Jun 18 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..64

Crossrefs

Cf. A258880 (k=3), A258901 (k=4), A258925 (k=5), A258927 (k=6), A259113 (k=8).

Programs

PARI

{a(n) = local(A=x); A = serreverse( intformal( 1/(1 + x^7 + O(x^(7*n+2))) ) ); (7*n+1)!*polcoeff(A, 7*n+1)}
for(n=0, 20, print1(a(n), ", ")) \\ after Paul D. Hanna

Formula

a(n) ~ 7^(7*n+7/3) * n^(1/6) * (sin(Pi/7)/Pi)^(7*n+7/6) * (7*n)! / (6^(1/6) * Gamma(1/6)).