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A000987 Number of stochastic matrices of integers.
(Formerly M1793 N0707)
1
0, 1, 1, 2, 7, 32, 184, 1268, 10186, 93356, 960646, 10959452, 137221954, 1870087808, 27548231008, 436081302248, 7380628161076, 132975267434552, 2540593483517404, 51299775805464824, 1091447620966600804, 24401984084483685248, 571907754141520643296 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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
H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), vol 3, 653-659.
H. Gupta, Enumeration of symmetric matrices (annotated scanned copy).
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
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 *)
CROSSREFS
Sequence in context: A000153 A006154 A352435 * A006957 A189780 A195983
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Sep 24 2015
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)