A000987 Number of stochastic matrices of integers.

0, 1, 1, 2, 7, 32, 184, 1268, 10186, 93356, 960646, 10959452, 137221954, 1870087808, 27548231008, 436081302248, 7380628161076, 132975267434552, 2540593483517404, 51299775805464824, 1091447620966600804, 24401984084483685248, 571907754141520643296

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• John Cerkan, Table of n, a(n) for n = 0..445
• H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), vol 3, 653-659.
• H. Gupta, Enumeration of symmetric matrices (annotated scanned copy).

Programs

Mathematica

(* b = A000985 *) Clear[a, b]; b[0] = 1; b[1] = 1; b[2] = 3; b[3] = 11; b[4] = 56; b[n_] := b[n] = (2*n-1)*b[n-1] - (n-2)*(n-1)*b[n-2] - (n-2)*(n - 1)*b[n-3] + (n-3)*(n-2)*(n-1)*b[(n-4)]/2; a[0] = 0; a[1] = 1; a[n_] := a[n] = (n-2)*a[n-1] + b[n-2]; Array[a, 22, 0] (* Jean-François Alcover, Feb 15 2016, after Sean A. Irvine *)

Formula

a(0) = 0, a(1) = 1, a(n) = (n-2) * a(n-1) + A000985(n - 2), n >= 2. - Sean A. Irvine, Sep 24 2015

Extensions

More terms from Sean A. Irvine, Sep 24 2015