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 A303652 Column sums of irregular triangle A303650. 2

%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.: (1-x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1-x)^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)/(1-x)^2 = 1 + 3*x*(2-2*x+x^2) + 5*x^2*(2-2*x+x^2)^3 + 7*x^3*(2-2*x+x^2)^6 + 9*x^4*(2-2*x+x^2)^10 + 11*x^5*(2-2*x+x^2)^15 + 13*x^6*(2-2*x+x^2)^21 +...

%o (PARI) {a(n) = my(A = (1-x)^2 * sum(m=0,n, (2*m+1) * x^m * (1 + (1-x)^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

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)