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A051256 Numbers formed from binomial coefficients (mod 2) interpreted as digits in factorial base. 3
1, 3, 7, 33, 121, 843, 5167, 46233, 362881, 3991683, 40279687, 522910113, 6227383801, 93409304523, 1313941673647, 22324392524313, 355687428096001, 6758061133824003, 122000787836928007, 2561305169719296033 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..448

FORMULA

a(n) = Sum_{k=0..n} (k+1)!(C(n, k) mod 2).

EXAMPLE

a(5) = 1! + 2! + 5! + 6! = 843 (only the first, second, fifth and sixth terms are odd in row 5 of Pascal's Triangle).

MAPLE

A051256(n) := proc(n) local i; RETURN(add(((binomial(n, i) mod 2)*((i+1)!)), i=0..n)); end;

MATHEMATICA

Table[Sum[(k+1)!Mod[Binomial[n, k], 2], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Feb 14 2013 *)

PROG

(Python)

from math import factorial

def A051256(n):

    return sum(0 if ~n & k else factorial(k+1) for k in range(n+1)) # Chai Wah Wu, Feb 08 2016

CROSSREFS

Cf. A001317, A001339, A048757, A047999.

Sequence in context: A238314 A120566 A057480 * A057795 A054935 A208989

Adjacent sequences:  A051253 A051254 A051255 * A051257 A051258 A051259

KEYWORD

nonn,nice,base

AUTHOR

Antti Karttunen, Oct 24 1999

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)