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A259476 Cayley's triangle of V numbers. 1
1, 2, 4, 3, 14, 14, 4, 32, 72, 48, 5, 60, 225, 330, 165, 6, 100, 550, 1320, 1430, 572, 7, 154, 1155, 4004, 7007, 6006, 2002, 8, 224, 2184, 10192, 25480, 34944, 24752, 7072, 9, 312, 3822, 22932, 76440, 148512, 167076, 100776, 25194, 10, 420, 6300, 47040, 199920, 514080, 813960, 775200, 406980, 90440, 11, 550, 9900, 89760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Table of n, a(n) for n=4..62.

A. Cayley, On the partitions of a polygon, Proc. London Math. Soc., 22 (1891), 237-262 = Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.

EXAMPLE

Triangle begins:

1,

2,4,

3,14,14,

4,32,72,48,

5,60,225,330,165,

6,100,550,1320,1430,572,

...

MAPLE

V := proc(n, x)

    local X, g, i ;

    X := x^2/(1-x) ;

    g := X^n ;

    for i from 1 to n-2 do

        g := diff(g, x) ;

    end do;

    x^2*g*2*(n-1)/n! ;

end proc;

A259476 := proc(n, k)

    V(k-n+2, x) ;

    coeftayl(%, x=0, n+2) ;

end proc:

for n from 4 to 14 do

    for k from n to 2*n-4 do

        printf("%d, ", A259476(n, k)) ;

    end do:

    printf("\n") ;

end do: # R. J. Mathar, Jul 09 2015

CROSSREFS

Diagonals give A002057, A002058, A002059, A002060.

Sequence in context: A079308 A189825 A271878 * A271363 A115399 A109429

Adjacent sequences:  A259473 A259474 A259475 * A259477 A259478 A259479

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jul 03 2015

STATUS

approved

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Last modified April 5 02:11 EDT 2020. Contains 333238 sequences. (Running on oeis4.)