A213887 Triangle of coefficients of representations of columns of A213743 in binomial basis.

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 0, 4, 6, 4, 1, 0, 0, 3, 10, 10, 5, 1, 0, 0, 2, 12, 20, 15, 6, 1, 0, 0, 1, 12, 31, 35, 21, 7, 1, 0, 0, 0, 10, 40, 65, 56, 28, 8, 1, 0, 0, 0, 6, 44, 101, 120, 84, 36, 9, 1, 0

Offset

0,9

Comments

This triangle is the third array in the sequence of arrays A026729, A071675 considered as triangles.

Let {a_(k,i)}, k>=1, i=0,...,k, be the k-th row of the triangle. 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.

Riordan array (1,x+x^2+x^3+x^4). A186332 with additional 0 column. - _Ralf Stephan_, Dec 31 2013

Links

Table of n, a(n) for n=0..66.

Example

As a triangle, this begins
n/k.|..0....1....2....3....4....5....6....7....8....9
=====================================================
.0..|..1
.1..|..0....1
.2..|..0....1....1
.3..|..0....1....2....1
.4..|..0....1....3....3....1
.5..|..0....0....4....6....4....1
.6..|..0....0....3...10...10....5....1
.7..|..0....0....2...12...20...15....6....1
.8..|..0....0....1...12...31...35...21....7....1
.9..|..0....0....0...10...40...65...56...28....8....1

Crossrefs

Cf. A026729, A071675.

Sequence in context: A121480 A082601 A286509 * A279589 A279594 A335162

Adjacent sequences: A213884 A213885 A213886 * A213888 A213889 A213890

Keyword

nonn,tabl

Author

_Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 23 2012

Status

approved