A132428 Central terms of triangle A132427.
1, 1, 3, 10, 43, 216, 1241, 7988, 56763, 440254, 3693728, 33281359, 320112326, 3270177860, 35329070470, 402128329243, 4806784533967, 60166803598106, 786622663286330, 10717555856584617, 151864784070048105
Offset: 0
Programs
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Maxima
a(n):=if n=0 then 1 else sum(sum(binomial(i-1,k-1)*binomial(i,n-i),i,k,n)*a(k-1),k,1,n); /* Vladimir Kruchinin, May 02 2012 */
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PARI
{a(n)=local(G=1+x+x*O(x^n));for(i=0,n,G=1+x*subst(G,x,x/(1-x)^2)/(1-x)); polcoeff(subst((G-1)/x,x,x/(1+x))/(1+x),n)}
Formula
Binomial transform equals A125273.
a(n)=sum(k=1..n, sum(i=k..n, binomial(i-1,k-1)*binomial(i,n-i))*a(k-1)), n>0,a(0)=1. [Vladimir Kruchinin, May 02 2012]