A355991
a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)!).
Original entry on oeis.org
1, 2, 5, 12, 57, 158, 1101, 5442, 28811, 212502, 2337513, 9422306, 122489967, 1654319046, 13917499277, 111631450818, 1897734663891, 23705612782022, 450406642858401, 3091477152208002, 51404897928720023, 1130752882197523686, 26007316290543044757
Offset: 1
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a[n_] := n! * Sum[1/(k! * Floor[n/k]!), {k, 1, n}]; Array[a, 23] (* Amiram Eldar, Jul 22 2022 *)
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a(n) = n!*sum(k=1, n, 1/(k!*(n\k)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (1-x^k)*(exp(x^k)-1)/k!)/(1-x)))
A355989
a(n) = n! / (2 * floor(n/2)!).
Original entry on oeis.org
1, 3, 6, 30, 60, 420, 840, 7560, 15120, 166320, 332640, 4324320, 8648640, 129729600, 259459200, 4410806400, 8821612800, 167610643200, 335221286400, 7039647014400, 14079294028800, 323823762662400, 647647525324800, 16191188133120000, 32382376266240000
Offset: 2
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a[n_] := n!/(2 * Floor[n/2]!); Array[a, 25, 2] (* Amiram Eldar, Jul 22 2022 *)
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a(n) = n!/(2*(n\2)!);
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2)*(exp(x^2)-1)/(2*(1-x))))
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from math import factorial, floor
def a(n): return int(factorial(n)/(2*factorial(floor(n/2))))
print([a(n) for n in range(2, 30)]) # Javier Rivera Romeu, Jul 22 2022
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from sympy import rf
def A355989(n): return rf((m:=n+1>>1)+(n+1&1),m)>>1 # Chai Wah Wu, Jul 22 2022
A355990
a(n) = n! / (6 * floor(n/3)!).
Original entry on oeis.org
1, 4, 20, 60, 420, 3360, 10080, 100800, 1108800, 3326400, 43243200, 605404800, 1816214400, 29059430400, 494010316800, 1482030950400, 28158588057600, 563171761152000, 1689515283456000, 37169336236032000, 854894733428736000, 2564684200286208000
Offset: 3
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a[n_] := n!/(6 * Floor[n/3]!); Array[a, 22, 3] (* Amiram Eldar, Jul 22 2022 *)
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a(n) = n!/(6*(n\3)!);
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)*(exp(x^3)-1)/(6*(1-x))))
A356013
Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).
Original entry on oeis.org
1, 1, 1, 2, 3, 1, 6, 6, 4, 1, 24, 30, 20, 5, 1, 120, 120, 60, 30, 6, 1, 720, 840, 420, 210, 42, 7, 1, 5040, 5040, 3360, 840, 336, 56, 8, 1, 40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1, 362880, 362880, 201600, 75600, 15120, 5040, 720, 90, 10, 1
Offset: 1
Triangle begins:
1;
1, 1;
2, 3, 1;
6, 6, 4, 1;
24, 30, 20, 5, 1;
120, 120, 60, 30, 6, 1;
720, 840, 420, 210, 42, 7, 1;
5040, 5040, 3360, 840, 336, 56, 8, 1;
40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1;
...
Showing 1-4 of 4 results.