cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A249269 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} x^k = Sum_{k=0..n} A_k*(x-3*(-1)^k)^k.

Original entry on oeis.org

1, -2, 1, -29, 7, 1, 268, -74, -8, 1, 4885, -1262, -170, 13, 1, -82838, 21823, 2800, -257, -14, 1, -2097065, 548161, 72055, -6197, -419, 19, 1, 51727192, -13551428, -1770128, 155398, 9976, -548, -20, 1, 1696812649, -444145484, -58168484, 5067886, 333166, -17180, -776, 25, 1
Offset: 0

Views

Author

Derek Orr, Oct 23 2014

Keywords

Comments

Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x-3)^0 + A_1*(x+3)^1 + A_2*(x-3)^2 + A_3*(x+3)^3 + ... + A_n*(x-3*(-1)^n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.

Examples

			Triangle starts:
1;
-2,                  1;
-29,                 7,         1;
268,               -74,        -8,       1;
4885,            -1262,      -170,      13,      1;
-82838,          21823,      2800,    -257,    -14,      1;
-2097065,       548161,     72055,   -6197,   -419,     19,    1;
51727192,    -13551428,  -1770128,  155398,   9976,   -548,  -20,  1;
1696812649, -444145484, -58168484, 5067886, 333166, -17180, -776, 25, 1;
...

Crossrefs

Cf. A248978, A248976.

Programs

  • PARI
    a(n, j, L)=if(j==n, return(1)); if(j!=n, return(1-sum(i=1, n-j, (-L)^i*(-1)^(i*j)*binomial(i+j, i)*a(n, i+j, L))))
for(n=0, 10, for(j=0, n, print1(a(n, j, -3), ", ")))
Showing 1-1 of 1 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.