A117927 a(n) = binomial(s(n), n) where s(n) = n-th semiprime.

4, 15, 84, 210, 2002, 5005, 116280, 319770, 2042975, 5311735, 193536720, 548354040, 1476337800, 9669554100, 25140840660, 991493848554, 6499270398159, 27900908274925, 280576272201225, 1210269541711230, 3342649210440540, 34315056105966195, 227068876035237600, 2305629203680278840

Offset

1,1

Comments

Semiprime analog of A060604.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = binomial(A001358(n), n).

Example

a(1) = binomial(4,1) = 4.
a(2) = binomial(6,2) = 15.
a(3) = binomial(9,3) = 84.
a(4) = binomial(10,4) = 210.
a(5) = binomial(14,5) = 2002.
a(6) = binomial(15,6) = 5005.
a(7) = binomial(21,7) = 116280.
a(8) = binomial(22,8) = 319770.
a(9) = binomial(25,9) = 2042975.
a(10) = binomial(26,10) = 5311735.

Mathematica

Binomial[First[#], Last[#]]&/@With[{sprs=Select[Range[70], PrimeOmega[#] == 2&]}, Thread[{sprs, Range[Length[sprs]]}]] (* Harvey P. Dale, Aug 10 2012 *)

Prog

(PARI) s(n) = my(k=1, nb=0); while (nb != n, if (bigomega(k)==2, nb++); if (nb != n, k++)); k; \\ A001358
a(n) = binomial(s(n), n); \\ Michel Marcus, Jul 15 2022

Crossrefs

Cf. A001358, A060604.

Sequence in context: A232220 A129653 A081722 * A143340 A151379 A130679

Adjacent sequences: A117924 A117925 A117926 * A117928 A117929 A117930

Keyword

easy,nonn

Author

Jonathan Vos Post, May 03 2006

Extensions

More terms from Michel Marcus, Jul 15 2022

Status

approved