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G.f.: Sum_{n>=0} x^n / Product_{k=n*(n-1)/2+1..n*(n+1)/2} (1 - k*x).
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%I #5 Nov 09 2014 13:44:59

%S 1,1,2,7,36,252,2278,25479,343318,5455963,100504720,2117265242,

%T 50438185262,1345840435641,39899564488618,1305139816260887,

%U 46817884128344164,1831903983379048308,77815287718736660334,3573159363560866942735,176687138080525842904446,9376097634171921557906827

%N G.f.: Sum_{n>=0} x^n / Product_{k=n*(n-1)/2+1..n*(n+1)/2} (1 - k*x).

%H Vaclav Kotesovec, <a href="/A249637/b249637.txt">Table of n, a(n) for n = 0..310</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 252*x^5 + 2278*x^6 +...

%e where

%e A(x) = 1 + x/(1-x) + x^2/((1-2*x)*(1-3*x)) + x^3/((1-4*x)*(1-5*x)*(1-6*x)) + x^4/((1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)) + x^5/((1-11*x)*(1-12*x)*(1-13*x)*(1-14*x)*(1-15*x)) +...

%o (PARI) {a(n)=polcoeff(sum(m=0,n,x^m/prod(k=m*(m-1)/2+1,m*(m+1)/2,1-k*x +x*O(x^n))),n)}

%o for(n=0,30,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 02 2014