A048644 -id:A048644

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A048643

Differences between partial products of Gray code (A048642) and factorials (A000142).

+10
1

0, 0, 1, 0, 12, 132, 540, 0, 20160, 423360, 8164800, 125193600, 1172102400, 11935123200, 76281004800, 0, 10461394944000, 428917192704000, 14781951055872000, 429147343392768000, 14090871305871360000, 461146030563778560000, 13730871481551544320000, 390084405122331279360000

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OFFSET

0,5

COMMENTS

a((2^n)-1) = 0 for all n.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(0) = 0, a(n) = product(XORnos(j, floor(j/2)), j=1..n) - n!.

a(n) = A048642(n) - A000142(n).

PROG

(PARI) a(n) = prod(i=1, n, bitxor(i, i>>1)) - n!; \\ Michel Marcus, Oct 02 2015

CROSSREFS

Cf. A000142, A048642, A048644.

KEYWORD

easy,nonn

AUTHOR

Antti Karttunen, Jul 14 1999

EXTENSIONS

More terms from Michel Marcus, Oct 02 2015

STATUS

approved

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