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

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• tabl

Examples

			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.

Formula

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