login
A060935
Sum of entries in n-th antidiagonal in A060854.
1
1, 2, 4, 12, 72, 1010, 36302, 3501500, 984382830, 820391106394, 2231837962830894, 19443994569352596154, 611248544067759392038426, 65374059149370152526265388842, 27613396368509694864033710442373202
OFFSET
1,2
LINKS
FORMULA
a(n) ~ c(n) * sqrt(Pi) * exp(7/12 + n/2 + n^2/8) * n^(11/12 + n/2 + n^2/4) / (A * 2^(5/6 + 3*n/2 + 3*n^2/4)), where c(n) = 2 if n is even and c(n) = (n/2)^(1/4) if n is odd, A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 29 2023
MAPLE
T:= (m, n)-> (m*n)! * mul(i!/(m+i)!, i=0..n-1):
a:= n-> add (T(k, 1+n-k), k=1..n):
seq (a(n), n=1..20); # Alois P. Heinz, Aug 06 2012
MATHEMATICA
A060854[n_, k_]:= (k*(n-k+1))!*BarnesG[k+1]*BarnesG[n-k+2]/BarnesG[n+2];
Table[Sum[A060854[n, k], {k, n}], {n, 20}] (* G. C. Greubel, Apr 07 2021 *)
PROG
(Magma)
A060854:= func< n, k | Factorial((n-k+1)*k)*(&*[ Factorial(j)/Factorial(n-k+j+1): j in [0..k-1] ]) >;
[(&+[ A060854(n, k): k in [1..n] ]): n in [1..20]]; // G. C. Greubel, Apr 07 2021
(Sage)
def A060854(n, k): return factorial((n-k+1)*k)*product( factorial(j)/factorial(n-k+j+1) for j in (0..k-1) )
def A060935(n): return sum( A060854(n, k) for k in (1..n) )
[A060935(n) for n in (1..20)] # G. C. Greubel, Apr 07 2021
CROSSREFS
Cf. A060854.
Sequence in context: A078919 A372994 A085864 * A141522 A114903 A038054
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 06 2001
EXTENSIONS
More terms from Frank Ellermann, Jun 15 2001
STATUS
approved