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A213887 Triangle of coefficients of representations of columns of A213743 in binomial basis. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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 A077593

Adjacent sequences:  A213884 A213885 A213886 * A213888 A213889 A213890

KEYWORD

nonn,tabl

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Jun 23 2012

STATUS

approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)