OFFSET
0,7
COMMENTS
These are the telephone numbers T^(6)_n of [Artioli et al., p. 7].
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..524
Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi, and Simonetta Pagnutti, Motzkin Numbers: an Operational Point of View, arXiv:1703.07262 [math.CO], 2017.
FORMULA
a(n) = a(n-1) + (n-1)!/(n-6)! * a(n-6).
a(n) = Sum_{j=0..floor(n/6)} n!/(6^j*j!*(n-6*j)!). - G. C. Greubel, Mar 07 2021
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[x+x^6/6], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 11 2017 *)
Table[Sum[n!/(6^k*k!*(n-6*k)!), {k, 0, n/6}], {n, 0, 30}] (* G. C. Greubel, Mar 07 2021 *)
PROG
(PARI) my(x = 'x + O('x^30)); Vec(serlaplace(exp(x + x^6/6))) \\ Michel Marcus, Oct 13 2017
(Sage)
f=factorial;
[sum( f(n)/(6^k*f(k)*f(n-6*k)) for k in [0..n/3]) for n in [0..30]] # G. C. Greubel, Mar 07 2021
(Magma)
F:= Factorial;
[(&+[ F(n)/(6^k*F(k)*F(n-6*k)): k in [0..Floor(n/3)]]): n in [0..30]]; // G. C. Greubel, Mar 07 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Oct 12 2017
STATUS
approved