A046757 Triangle of coefficients of certain polynomials (exponents in decreasing order).

1, 2, 1, 5, 5, 1, 30, 30, 10, 1, 272, 272, 102, 17, 1, 3250, 3250, 1300, 260, 26, 1, 47952, 47952, 19980, 4440, 555, 37, 1, 840350, 840350, 360150, 85750, 12250, 1050, 50, 1, 17039360, 17039360, 7454720, 1863680, 291200, 29120, 1820, 65, 1, 392203458

Offset

0,2

Links

Table of n, a(n) for n=0..45.

Formula

a(n, n) = 1, a(n, m) = (1+n^2)*binomial(n, m)*n^(n-m-2), n>m >= 0, else 0.

Example

Triangle begins:
  {1};
  {2,1};
  {5,5,1};
  {30,30,10,1};
  {272,272,102,17,1};
  ....
E.g. third row {5,5,1} corresponds to polynomial q(3,x)= 5*x^2+5*x+1.

Crossrefs

x*p(k-1, -x)/q(k, -x), with the row polynomials p(n, x) from triangle A033842(n, m) is for k=1..5 g.f. for A000079 (powers of two), A039717, A043553, A045624, A046088, respectively.

Sequence in context: A248727 A270250 A204119 * A248905 A118244 A108410

Adjacent sequences: A046754 A046755 A046756 * A046758 A046759 A046760

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved