A062747 - OEIS

%I #13 Mar 27 2020 02:56:41

%S 1,7,89,1447,26713,532391,11165785,242851751,5427716185,123901026215,

%T 2876525797465,67710590623655,1612262780199001,38764533106581415,

%U 939825790848884825,22950405085586497447

%N Row sums of (unsigned) staircase array A062746.

%F a(n)=N(3; k, x=-1), with the polynomials N(3; k, x) from the staircase array A062746.

%F a(n) = 2*( Sum_{j = 0..n} (-1)^j*C(3; n-j)*4^(n-j) ) - (-1)^n with C(3; n) := A001764(n) = A062993(n+1, 1) (a Pfaff-Fuss or 3-Raney sequence).

%F G.f.: (2*c(3; 4*x)-1)/(1+x) with c(3; x)= RootOf(x*_Z^3-_Z +1), the g.f. of A001764 [formula for a(n) and g.f. corrected by _Peter Bala_, Mar 26 2020].

%F Conjectural recurrence: n*(2*n+1)*a(n) = (4*n-3)*(13*n-4)*a(n-1) + 6*(3*n-1)*(3*n-2)*a(n-2) with a(0) = 1, a(1) = 7. - _Peter Bala_, Mar 25 2020

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 12 2001