The On-Line Encyclopedia of Integer Sequences (OEIS)

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A119329

Number triangle T(n,k)=sum{j=0..n-k, C(k,2j)C(n-k,2j)*2^j}.
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:59:15 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, May 14 2006

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#1 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

NAME

Number triangle T(n,k)=sum{j=0..n-k, C(k,2j)C(n-k,2j)*2^j}.

DATA

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 13, 19, 13, 1, 1, 1, 1, 21, 37, 37, 21, 1, 1, 1, 1, 31, 61, 77, 61, 31, 1, 1, 1, 1, 43, 91, 141, 141, 91, 43, 1, 1, 1, 1, 57, 127, 241, 301, 241, 127, 57, 1, 1

OFFSET

0,13

COMMENTS

Row sums are A119330. Product of Pascal's triangle A007318 and A119331. T(n,k)=T(n,n-k).

FORMULA

Column k has g.f. (x^k/(1-x))*sum{j=0..k, C(k,2j)*2^j*(x/(1-x))^(2j)}

EXAMPLE

Triangle begins

1,

1, 1,

1, 1, 1,

1, 1, 1, 1,

1, 1, 3, 1, 1,

1, 1, 7, 7, 1, 1,

1, 1, 13, 19, 13, 1, 1,

1, 1, 21, 37, 37, 21, 1, 1

CROSSREFS

Cf. A119326.

KEYWORD

easy,nonn,tabl,new

AUTHOR

Paul Barry (pbarry(AT)wit.ie), May 14 2006

STATUS

approved