1,1

This is to A003987 "Table of n XOR m (or Nim-sum of n and m)" as A007188 "Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i)" is to A007318 "Pascal's triangle read by rows." T[2i,2j] = 2T[i,j], T[2i+1,2j] = 2T[i,j] + 1. a(2^n-1) = (n#)^(2^n-1) = A002110(n)^A000225(n).

a(n) = Prod[i=i..n] p(i+1)^BitXOR(n,i).

a(1) = p(1)^T(1,1) = 2^1 = 2, where T(i,j) is as in A003987.

a(2) = p(1)^T(2,1) * p(2)^T(2,2) = 2^1 * 3^1 = 6.

a(3) = p(1)^T(3,1) * p(2)^T(3,2) * p(3)^T(3,3) = 2^2 * 3^0 * 5^2 = 100.

a(4) = 2^3 * 3^3 * 5^3 * 7^3 = 9261000.

a(5) = 2^4 * 3^2 * 5^0 * 7^2 * 11^4 = 103306896.

a(6) = 2^5 * 3^5 * 5^1 * 7^1 * 11^5 * 13^5 = 16274381169926880.

a(7) = 2^6 * 3^4 * 5^6 * 7^0 * 11^6 * 13^4 * 17^6 = 98925457477919384169000000.

a(8) = 2^7 * 3^7 * 5^7 * 7^7 * 11^7 * 13^7 * 17^7 * 19^7.

a(9) = 2^8 * 3^6 * 5^4 * 7^6 * 11^0 * 13^6 * 17^4 * 19^6 * 23^8.

a(10) = 2^9 * 3^9 * 5^5 * 7^5 * 11^1 * 13^1 * 17^5 * 19^5 * 23^9 * 29^9.

Cf. A000040, A000225, A002110, A003987, A007188, A007318, A009766, A124061.

Adjacent sequences: A123254 A123255 A123256 this_sequence A123258 A123259 A123260

Sequence in context: A081992 A066091 A100704 this_sequence A054247 A099790 A059088

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 06 2006