cp's OEIS Frontend

A229675 a(n) = Sum_{k = 0..n} Product_{j = 0..7} C(n+j*k,k).

%I A229675 #16 Oct 11 2018 20:05:16
%S A229675 1,40321,81730010881,369400348294790401,2390471064720364776796801,
%T A229675 18975660656355118819906214670721,
%U A229675 171890067585060168829713844899790066561,1707759022485971054271963683059722310362986881,18165821273625565354157327818616137066973745155992321
%N A229675 a(n) = Sum_{k = 0..n} Product_{j = 0..7} C(n+j*k,k).
%C A229675 Number of lattice paths from {n}^8 to {0}^8 using steps that decrement one component or all components by 1.
%H A229675 Alois P. Heinz, <a href="/A229675/b229675.txt">Table of n, a(n) for n = 0..100</a>
%F A229675 a(n) = Sum_{k = 0..n} multinomial(n+7*k; n-k, {k}^8).
%F A229675 G.f.: Sum_{k >= 0} (8*k)!/k!^8 * x^k / (1-x)^(8*k+1).
%F A229675 exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 20161*x^2 + 27243357121*x^3 + 92350114520267521*x^4 + ... appears to have integer coefficients. - _Peter Bala_, Jan 13 2016
%p A229675 with(combinat):
%p A229675 a:= n-> add(multinomial(n+7*k, n-k, k$8), k=0..n):
%p A229675 seq(a(n), n=0..10);
%t A229675 multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[multinomial[n + 7*k, Join[{n - k}, Array[k&, 8]]], {k, 0, n}]; Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Dec 27 2013, translated from Maple *)
%t A229675 Table[Sum[Product[Binomial[n+j*k,k],{j,0,7}],{k,0,n}],{n,0,10}] (* _Harvey P. Dale_, Aug 25 2014 *)
%Y A229675 Column k = 8 of A229142.
%K A229675 nonn,easy
%O A229675 0,2
%A A229675 _Alois P. Heinz_, Sep 27 2013