login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119307 Number triangle T(n,k)=sum{j=0..n, C(j,k)C(j,n-k)}. 2
1, 1, 1, 1, 5, 1, 1, 11, 11, 1, 1, 19, 46, 19, 1, 1, 29, 127, 127, 29, 1, 1, 41, 281, 517, 281, 41, 1, 1, 55, 541, 1579, 1579, 541, 55, 1, 1, 71, 946, 4001, 6376, 4001, 946, 71, 1, 1, 89, 1541, 8889, 20626, 20626, 8889, 1541, 89, 1, 1, 109, 2377, 17907, 56904, 82994 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
T(n,k)=T(n,n-k). Second column is A028387. Row sums are A014300. Central coefficients T(2n,n) are A112029.
LINKS
Indranil Ghosh, Rows 0..100, flattened
EXAMPLE
Triangle begins
1,
1, 1,
1, 5, 1,
1, 11, 11, 1,
1, 19, 46, 19, 1,
1, 29, 127, 127, 29, 1,
1, 41, 281, 517, 281, 41, 1
MATHEMATICA
Flatten[Table[Sum[Binomial[j, k] Binomial[j, n-k], {j, 0, n}], {n, 0, 10}, {k, 0, n}]] (* Indranil Ghosh, Mar 03 2017 *)
PROG
(PARI)
tabl(nn)={for (n=0, nn, for(k=0, n, print1(sum(j=0, n, binomial(j, k)*binomial(j, n-k)), ", "); ); print(); ); };
tabl(10); \\ Indranil Ghosh, Mar 03 2017
CROSSREFS
Sequence in context: A082046 A132787 A181370 * A296039 A296974 A146954
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, May 13 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)