OFFSET
0,2
COMMENTS
Number of lattice paths from {n}^9 to {0}^9 using steps that decrement one component or all components by 1.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
FORMULA
a(n) = Sum_{k = 0..n} multinomial(n+8*k; n-k, {k}^9).
G.f.: Sum_{k >= 0} (9*k)!/k!^9 * x^k / (1-x)^(9*k+1).
exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 181441*x^2 + 4168213439041*x^3 + 270123052269252349441*x^4 + ... appears to have integer coefficients. - Peter Bala, Jan 13 2016
MAPLE
with(combinat):
a:= n-> add(multinomial(n+8*k, n-k, k$9), k=0..n):
seq(a(n), n=0..10);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[multinomial[n + 8*k, Join[{n - k}, Array[k&, 9]]], {k, 0, n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 27 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 27 2013
STATUS
approved