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A303652
Column sums of irregular triangle A303650.
2
1, 4, 23, 269, 6080, 263107, 21755790, 3448734174, 1054337703035, 625864795912552, 726009710371573669, 1654701176883966564948, 7441600457415936633083792, 66248198041546539808288183964, 1170186904620869164091169463554964, 41080483613395453869669149072267922983
OFFSET
0,2
FORMULA
G.f.: (1-x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1-x)^2)^(n*(n+1)/2).
EXAMPLE
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 +...
PROG
(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), ", "))
CROSSREFS
Sequence in context: A293510 A234595 A327367 * A130890 A219932 A266919
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 30 2018
STATUS
approved