%I
%S 1,4,23,269,6080,263107,21755790,3448734174,1054337703035,
%T 625864795912552,726009710371573669,1654701176883966564948,
%U 7441600457415936633083792,66248198041546539808288183964,1170186904620869164091169463554964,41080483613395453869669149072267922983
%N Column sums of irregular triangle A303650.
%F G.f.: (1x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1x)^2)^(n*(n+1)/2).
%e G.f.: A(x) = 1 + 4*x + 23*x^2 + 269*x^3 + 6080*x^4 + 263107*x^5 + 21755790*x^6 + 3448734174*x^7 + 1054337703035*x^8 + ...
%e such that
%e A(x)/(1x)^2 = 1 + 3*x*(22*x+x^2) + 5*x^2*(22*x+x^2)^3 + 7*x^3*(22*x+x^2)^6 + 9*x^4*(22*x+x^2)^10 + 11*x^5*(22*x+x^2)^15 + 13*x^6*(22*x+x^2)^21 +...
%o (PARI) {a(n) = my(A = (1x)^2 * sum(m=0,n, (2*m+1) * x^m * (1 + (1x)^2 +x*O(x^n) )^(m*(m+1)/2) ) ); polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A303650, A303651.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 30 2018
