A294214 E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)) - 1).

1, 1, 5, 31, 241, 2261, 25501, 319915, 4564001, 71905321, 1240694101, 23250921431, 470598127825, 10200501671101, 236040247113581, 5800885227542371, 150850086300786241, 4137020164029442385, 119309846230265324581, 3608164806033723494671

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..430

Formula

a(n) = a(n-1) + 2*(n-1)*n*a(n-2) + (n-2)*(n-1)*(2*n+1)*a(n-3) - (n-10)*(n-3)*(n-2)*(n-1)*a(n-4) - 4*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + 2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7) + 2*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-8) - (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-10). - Vaclav Kotesovec, Dec 02 2021

a(n) ~ exp(-101/144 + 29*n^(1/4)/(36*2^(3/4)) + sqrt(n/2) + 2^(7/4)*n^(3/4)/3 - n) * n^(n - 1/8) / 2^(9/8) * (1 + 71323/(103680*2^(1/4)*n^(1/4))). - Vaclav Kotesovec, Dec 02 2021

Mathematica

nmax = 20; CoefficientList[Series[E^(1/((1-x)*(1-x^2)*(1-x^3)) - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Dec 02 2021 *)

Prog

(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2)*(1-x^3))-1)))

Crossrefs

Column k=3 of A294212.

Sequence in context: A186859 A331335 A082579 * A261498 A368320 A276312

Adjacent sequences: A294211 A294212 A294213 * A294215 A294216 A294217

Keyword

nonn

Author

Seiichi Manyama, Oct 25 2017

Status

approved