This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117207 Number triangle read by rows: T(n,k)=sum{j=0..n-k, C(n+j,j+k)C(n-j,k)}. 1
 1, 3, 1, 10, 7, 1, 35, 31, 13, 1, 126, 121, 81, 21, 1, 462, 456, 381, 181, 31, 1, 1716, 1709, 1583, 1058, 358, 43, 1, 6435, 6427, 6231, 5055, 2605, 645, 57, 1, 24310, 24301, 24013, 21661, 14605, 5785, 1081, 73, 1, 92378, 92368, 91963, 87643, 70003, 38251, 11791 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are A037965(n+1). Second column is A048775. - Paul Barry, Oct 01 2010 First column is A001700. - Dan Uznanski, Jan 23 2012 The number of different ordered partitions of n+1 into n+1 bins (as with A001700), such that more than k bins are nonempty. - Dan Uznanski, Jan 23 2012 Second diagonal is A002061. - Franklin T. Adams-Watters, Jan 24 2012 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 FORMULA T(n,k)=C(2n+1,n+1)-sum{j=1..k, product{i=0..j-2, (n-i)^2}/((j-1)!j!)}}*(n+1). T(n,k)=[x^(n-k)](1+x)^(n-k)*F(-n-1,-n,1,x/(1+x)). - Paul Barry, Oct 01 2010 T(n,k)=C(2n+1,n+1)-(n+1)*sum(j=1,k, C(n,j-1)^2/j). - M. F. Hasler, Jan 25 2012 EXAMPLE Triangle begins      1,      3,    1,     10,    7,    1,     35,   31,   13,    1,    126,  121,   81,   21,   1,    462,  456,  381,  181,  31,  1,   1716, 1709, 1583, 1058, 358, 43, 1 MATHEMATICA Table[Sum[Binomial[n+j, j+k]Binomial[n-j, k], {j, 0, n-k}], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Apr 23 2016 *) PROG (PARI) T(n, k)=sum(j=0, n-k, binomial(n+j, j+k)*binomial(n-j, k)) T(n, k)=binomial(2*n+1, n+1)-(n+1)*sum(j=1, k, binomial(n, j-1)^2/j) A117207(k)=my(n=sqrtint(2*k-sqrtint(2*k))); T(n, k-n*(n+1)/2) \\ M. F. Hasler, Jan 25 2012 CROSSREFS Sequence in context: A171568 A107056 A116384 * A046658 A124574 A322383 Adjacent sequences:  A117204 A117205 A117206 * A117208 A117209 A117210 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Mar 02 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 19:46 EDT 2019. Contains 323481 sequences. (Running on oeis4.)