The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A122175 Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k, n-k) for n>=k>=0. 5
 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 7, 1, 1, 5, 20, 28, 11, 1, 1, 6, 35, 84, 66, 16, 1, 1, 7, 56, 210, 286, 136, 22, 1, 1, 8, 84, 462, 1001, 816, 253, 29, 1, 1, 9, 120, 924, 3003, 3876, 2024, 435, 37, 1, 1, 10, 165, 1716, 8008, 15504, 12650, 4495, 703, 46, 1, 1, 11, 220 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Remarkably, column k of the matrix inverse (A121435) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 1). LINKS EXAMPLE Triangle begins: 1; 1, 1; 1, 2, 1; 1, 3, 4, 1; 1, 4, 10, 7, 1; 1, 5, 20, 28, 11, 1; 1, 6, 35, 84, 66, 16, 1; 1, 7, 56, 210, 286, 136, 22, 1; 1, 8, 84, 462, 1001, 816, 253, 29, 1; ... MATHEMATICA Table[Binomial[(k(k+1))/2+n-k, n-k], {n, 0, 20}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 22 2016 *) PROG (PARI) T(n, k)=if(n

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 September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)