A259473 Irregular triangle read by rows of coefficients arising in the enumeration of doubly stochastic matrices of integers, n >= 1, 0 <= k <= (n-1)*(n-2).

1, 1, 1, 1, 1, 1, 14, 87, 148, 87, 14, 1, 1, 103, 4306, 63110, 388615, 1115068, 1575669, 1115068, 388615, 63110, 4306, 103, 1, 1, 694, 184015, 15902580, 567296265, 9816969306, 91422589980, 490333468494, 1583419977390, 3166404385990, 3982599815746, 3166404385990

Offset: 1

Author

N. J. A. Sloane, Jul 03 2015

Keywords

• nonn
• tabf

Comments

The n-th row of A257493 is a polynomial of degree (n-1)^2. This triangle gives the coefficients of the numerator of the generating functions for A257493 with denominators being (1-x)^(1+(n-1)^2). - Andrew Howroyd, Apr 11 2020

Examples

			Triangle begins:
  1;
  1;
  1,1,1;
  1,14,87,148,87,14,1;
  1,103,4306,63110,388615,1115068,1575669,1115068,388615,63110,4306,103,1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..177 (rows 1..9)
• D. M. Jackson and G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4 (1975), 474-477, doi:10.1137/0204040.
• D. M. Jackson & G. H. J. van Rees, The enumeration of generalized double stochastic nonnegative integer square matrices, SIAM J. Comput., 4.4 (1975), 474-477. (Annotated scanned copy)

Crossrefs

Row sums are A037302.

Cf. A005466, A005467, A257493.

Formula

T(n,k) = Sum_{i=0..k} A257493(n, k-i)*(-1)^i*binomial(1+(n-1)^2,i). - Andrew Howroyd, Apr 11 2020

Extensions

a(1)=1 prepended and terms a(26) and beyond from Andrew Howroyd, Apr 11 2020