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Riordan array (1,x+x^2+x^3+x^4). A186332 with additional 0 column. - Ralf Stephan, Dec 31 2013
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Vladimir Shevelev and _Peter J. C. Moses._, _, Jun 23 2012
Vladimir Shevelev and _Peter J. C. Moses, ._, Jun 23 2012
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Array read by antidiagonals Triangle of quadrinomial coefficients of representations of columns of A213743 in binomial basis.
This array triangle is the third array in the sequence of arrays A026729, A071675,...Quadrinomial coefficients are coefficients of powers of x in (1+x+x^2+x^3)^n considered as triangles.
Let {a_(k,i)}, k>=1, i=0,...,k, be the k-th antidiagonal row of the arraytriangle. Then s_k(n)=sum{i=0,...,k}a_(k,i)* binomial(n,k) is the n-th element of the k-th column of A213743. For example, s_1(n)=binomial(n,1)=n is the first column of A213743 for n>1, s_2(n)=binomial(n,1)+binomial(n,2)is the second column of A213743 for n>1, etc. In particular (see comment in A213743), in cases k=6,7,8,9 s_k(n) is A064056(n+2), A064057(n+2), A064058(n+2), A000575(n+3) respectively.
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Let {a_(k,i)}, k>=1, i=0,...,k, be the k-th antidiagonal of the array. Then s_k(n)=sum{i=0,...,k}a_(k,i)* binomial(n,k) is the n-th element of the k-th column of A213743. For example, s_1(n)=binomial(n,1)=n is the first column of A213743 for n>1, s_2(n)=binomial(n,1)+binomial(n,2)is the second column of A213743 for n>1, etc. In particular (see comment in A213743), in cases k=6,7,8,9 s_k(n) is A064056(n+2), A064057(n+2), A064058(n+2), A000575(n+3) respectively.
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