cp's OEIS Frontend

A118403 Unsigned row sums of triangle A118401; a(n) = A118402(n^2-n+2), where A118402 is the row sums of triangle A118400.

%I A118403 #17 Dec 22 2024 09:05:41
%S A118403 1,1,3,5,9,15,23,33,45,59,75,93,113,135,159,185,213,243,275,309,345,
%T A118403 383,423,465,509,555,603,653,705,759,815,873,933,995,1059,1125,1193,
%U A118403 1263,1335,1409,1485,1563,1643,1725,1809,1895,1983,2073,2165,2259,2355
%N A118403 Unsigned row sums of triangle A118401; a(n) = A118402(n^2-n+2), where A118402 is the row sums of triangle A118400.
%H A118403 Muniru A Asiru, <a href="/A118403/b118403.txt">Table of n, a(n) for n = 0..10000</a>
%H A118403 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A118403 G.f.: A(x) = (1-2*x+2*x^2)*(1+x^2)/(1-x)^3.
%F A118403 a(n) = A027688(n-2) for n > 1. - _Jon Maiga_, Jan 02 2019
%F A118403 E.g.f.: exp(x)*(5 - 2*x + x^2) - 2*(2 + x). - _Stefano Spezia_, Dec 21 2024
%p A118403 seq(coeff(series((1-2*x+2*x^2)*(1+x^2)/(1-x)^3,x,n+1), x, n), n = 0 .. 55); # _Muniru A Asiru_, Jan 02 2019
%t A118403 Join[{1, 1}, Table[n^2 + n + 3, {n, 0, 47}]] (* _Jon Maiga_, Jan 02 2019 *)
%o A118403 (PARI) {a(n)=polcoeff((1-2*x+2*x^2)*(1+x^2)/(1-x+x*O(x^n))^3,n,x)}
%Y A118403 Cf. A027688, A118400, A118401, A118402.
%K A118403 nonn,easy
%O A118403 0,3
%A A118403 _Paul D. Hanna_, Apr 27 2006