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A319208 a(n) = 1*2*3*4*5*6*7 + 8*9*10*11*12*13*14 + 15*16*17*18*19*20*21 + ... + (up to n). 10
1, 2, 6, 24, 120, 720, 5040, 5048, 5112, 5760, 12960, 100080, 1240560, 17302320, 17302335, 17302560, 17306400, 17375760, 18697680, 45209520, 603353520, 603353542, 603354026, 603365664, 603657120, 611247120, 816480720, 6570915120, 6570915149, 6570915990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general, for sequences that multiply the first k natural numbers, and then add the product of the next k natural numbers (preserving the order of operations up to n), we have a(n) = Sum_{i=1..floor(n/k)} (k*i)!/(k*i-k)! + Sum_{j=1..k-1} (1-sign((n-j) mod k)) * (Product_{i=1..j} n-i+1). Here, k=7.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{i=1..floor(n/7)} (7*i)!/(7*i-7)! + Sum_{j=1..6} (1-sign((n-j) mod 7)) * (Product_{i=1..j} n-i+1).

EXAMPLE

a(1) = 1;

a(2) = 1*2 = 2;

a(3) = 1*2*3 = 6;

a(4) = 1*2*3*4 = 24;

a(5) = 1*2*3*4*5 = 120;

a(6) = 1*2*3*4*5*6 = 720;

a(7) = 1*2*3*4*5*6*7 = 5040;

a(8) = 1*2*3*4*5*6*7 + 8 = 5048;

a(9) = 1*2*3*4*5*6*7 + 8*9 = 5112;

a(10) = 1*2*3*4*5*6*7 + 8*9*10 = 5760;

a(11) = 1*2*3*4*5*6*7 + 8*9*10*11 = 12960;

a(12) = 1*2*3*4*5*6*7 + 8*9*10*11*12 = 100080;

a(13) = 1*2*3*4*5*6*7 + 8*9*10*11*12*13 = 1240560;

a(14) = 1*2*3*4*5*6*7 + 8*9*10*11*12*13*14 = 17302320;

a(15) = 1*2*3*4*5*6*7 + 8*9*10*11*12*13*14 + 15 = 17302335;

a(16) = 1*2*3*4*5*6*7 + 8*9*10*11*12*13*14 + 15*16 = 17302560; etc.

CROSSREFS

Cf. A093361, (k=1) A000217, (k=2) A228958, (k=3) A319014, (k=4) A319205, (k=5) A319206, (k=6) A319207, (k=7) this sequence, (k=8) A319209, (k=9) A319211, (k=10) A319212.

Sequence in context: A033645 A248769 A319547 * A276841 A273694 A138113

Adjacent sequences:  A319205 A319206 A319207 * A319209 A319210 A319211

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 13 2018

STATUS

approved

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Last modified July 4 10:57 EDT 2020. Contains 335446 sequences. (Running on oeis4.)