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A303652
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Column sums of irregular triangle A303650.
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2
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1, 4, 23, 269, 6080, 263107, 21755790, 3448734174, 1054337703035, 625864795912552, 726009710371573669, 1654701176883966564948, 7441600457415936633083792, 66248198041546539808288183964, 1170186904620869164091169463554964, 41080483613395453869669149072267922983
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1-x)^2)^(n*(n+1)/2).
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EXAMPLE
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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 + ...
such that
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 +...
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PROG
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(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)}
for(n=0, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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