A370888
a(n) = (n-1)*(2*(n-2)!+1).
Original entry on oeis.org
3, 6, 15, 52, 245, 1446, 10087, 80648, 725769, 7257610, 79833611, 958003212, 12454041613, 174356582414, 2615348736015, 41845579776016, 711374856192017, 12804747411456018, 243290200817664019, 4865804016353280020, 102181884343418880021, 2248001455555215360022, 51704033477769953280023, 1240896803466478878720024
Offset: 2
- Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
- Michael De Vlieger, Table of n, a(n) for n = 2..450
- Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 9.
A371217
The maximum deck size to perform Colm Mulcahy's n-card trick.
Original entry on oeis.org
1, 4, 15, 52, 197, 896, 4987, 33216, 257161, 2262124, 22241671, 241476060, 2867551117, 36960108680, 513753523571, 7659705147976, 121918431264273, 2063255678027668, 36991535865656959, 700377953116334788, 13963866589144933461, 292421219327021540176, 6417047546280200867819
Offset: 1
Suppose the deck consists of 4 cards (1,2,3,4), and the assistant gets two cards. If the two cards contain 4, the assistant hides 4 and signals it with the other card face down. If there is no 4, then the cards are a and a+1 modulo 3. The assistant hides a+1, and signals it with a.
- Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
- Colm Mulcahy, Mathematical card magic: fifty-two new effects, published by CRC press, 2013.
- Alois P. Heinz, Table of n, a(n) for n = 1..450
- Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 10.
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a:= proc(n) option remember; `if`(n<4, n*(n^2-2*n+2),
((11*n^2-66*n-61)*a(n-1) -(17*n^2-155*n+134)*a(n-2)
+(n-3)*(n-81)*a(n-3) +(n-4)*(5*n+26)*a(n-4))/(11*n-72))
end:
seq(a(n), n=1..23); # Alois P. Heinz, Mar 18 2024
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Table[1 + (k - 1)(2 Sum[Binomial[k - 1, i] (i - 1)!, {i, 1, k - 1}] + 1), {k, 20}]
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from math import factorial
def A371217(n): return n+((n-1)*sum(factorial(n-1)//((i+1)*factorial(n-i-2)) for i in range(n-1))<<1) # Chai Wah Wu, May 02 2024
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