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A094796 Triangle read by rows giving coefficients of polynomials arising in successive differences of central binomial numbers. 0
1, 3, 1, 9, 15, 6, 27, 108, 135, 42, 81, 594, 1539, 1530, 456, 243, 2835, 12555, 25245, 22122, 6120, 729, 12393, 83835, 281475, 482436, 383292, 101520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let D_0(n)=binomial(2*n,n) and D_{k+1}(n)=D_{k}(n+1)-D_{k}(n), then D_{k}(n)=binomial(2*n,n)*(n+1)*(n+2)*...*(n+k)*P_{k}(n) where P_{k} is a polynomial with integer coefficients of degree k.

LINKS

Table of n, a(n) for n=0..27.

EXAMPLE

Third difference of central binomial numbers is given by : D_3(n)=binomial(2*n,n)*(n+1)*(n+2)*(n+3)*(27*n^3 + 108*n^2 + 135*n + 42) and fourth row of triangle is 27,108,135,42

CROSSREFS

Sequence in context: A157399 A288852 A162749 * A056843 A076806 A111568

Adjacent sequences:  A094793 A094794 A094795 * A094797 A094798 A094799

KEYWORD

nonn,tabl

AUTHOR

Benoit Cloitre, Jun 11 2004

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)