A062747 Row sums of (unsigned) staircase array A062746.

1, 7, 89, 1447, 26713, 532391, 11165785, 242851751, 5427716185, 123901026215, 2876525797465, 67710590623655, 1612262780199001, 38764533106581415, 939825790848884825, 22950405085586497447

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

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).

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].

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

Crossrefs

Sequence in context: A359646 A371386 A295543 * A099719 A142995 A350937

Adjacent sequences: A062744 A062745 A062746 * A062748 A062749 A062750

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 12 2001

Status

approved