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A051304 Number of 4-element proper antichains of an n-element set. 2
0, 0, 0, 0, 5, 780, 41545, 1442910, 39400305, 923889960, 19550316665, 384954289170, 7196416532305, 129495073447740, 2264887575116985, 38775513868485030, 653195404307491505, 10869004241198535120, 179171681947204584505, 2932562923651659410490, 47737465871974206925905 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..825

FORMULA

a(n) = (1/4!) * (16^n -18*12^n +60*10^n -9*9^n -102*8^n +105*7^n -90*6^n +95*5^n -31*4^n -33*3^n +28*2^n -6).

G.f. x^4*( 5 +365*x -7935*x^2 +46885*x^3 -191420*x^4 +2285460*x^5 -14380560*x^6 +27216000*x^7 ) / ( (x-1) *(9*x-1) *(6*x-1) *(7*x-1) *(3*x-1) *(5*x-1) *(2*x-1) *(12*x-1) *(10*x-1) *(4*x-1) *(8*x-1) *(16*x-1) ). - R. J. Mathar, Jun 13 2013

MATHEMATICA

Table[(16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/4!, {n, 0, 50}] (* G. C. Greubel, Oct 07 2017 *)

PROG

(PARI) for(n=0, 50, print1((16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/4!, ", ")) \\ G. C. Greubel, Oct 07 2017

(MAGMA) [(16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/(24): n in [0..50]]; // G. C. Greubel, Oct 07 2017

CROSSREFS

Cf. A032263, A036239, A051112.

Sequence in context: A171269 A172890 A195612 * A297921 A298545 A298335

Adjacent sequences:  A051301 A051302 A051303 * A051305 A051306 A051307

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

EXTENSIONS

Terms a(16) onward added by G. C. Greubel, Oct 07 2017

STATUS

approved

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)