A104968 - OEIS

%I #6 Jun 09 2021 22:38:24

%S 1,2,4,6,6,12,22,32,34,52,100,150,170,266,438,640,766,1196,1996,2888,

%T 3210,4994,8534,12392,15106,22154,34366,52134,62148,96956,156396,

%U 217416,262062,394164,643908,950944,1150368,1689176,2600992,3767888,4840338

%N Absolute row sums of triangle A104967.

%H G. C. Greubel, <a href="/A104968/b104968.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Sum_{k=0..n} abs(A104967(n,k)).

%t A104967[n_, k_]:= A104967[n, k]= Sum[(-2)^j*Binomial[k+1, j]*Binomial[n-j, k], {j, 0, n-k}];

%t A104968[n_]:= A104968[n]= Sum[Abs[A104967[n, k]], {k,0,n}];

%t Table[A104968[n], {n, 0, 50}] (* _G. C. Greubel_, Jun 09 2021 *)

%o (PARI) {a(n)=local(X=x+x*O(x^n)); sum(k=0,n,abs(polcoeff(polcoeff((1-2*X)/(1-X-X*y*(1-2*X)),n,x),k,y)))}

%o (Sage)

%o @cached_function

%o def A104967(n,k): return sum( (-2)^j*binomial(k+1,j)*binomial(n-j,k) for j in (0..n-k))

%o def A104968(n): return sum( abs(A104967(n,k)) for k in (0..n))

%o [A104968(n) for n in (0..50)] # _G. C. Greubel_, Jun 09 2021

%Y Cf. A104967, A104969.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 30 2005