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A137216 Erlang C queues type triangular sequence based on A122525. 3
1, 1, 1, 2, 2, 3, 6, 9, 22, 41, 24, 64, 266, 708, 1486, 120, 625, 4536, 17457, 48088, 108129, 720, 7776, 100392, 563088, 2043864, 5709120, 13399176, 5040, 117649, 2739472, 22516209, 107972560, 375217945, 1053757584, 2544404617, 40320, 2097152, 89020752, 1076444064, 6831882992, 29566405440, 99420254352, 279663595232, 688833593904 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
T(n, k) = (1/n)*( n^n * k^(n+1) - n! * (k - 1) * Sum_{j=0..n} (n*k)^j/j! ), with T(n, 0) = n! and T(n, 1) = n^(n-1).
EXAMPLE
Triangle begins as:
1;
1, 1;
2, 2, 3;
6, 9, 22, 41;
24, 64, 266, 708, 1486;
120, 625, 4536, 17457, 48088, 108129;
720, 7776, 100392, 563088, 2043864, 5709120, 13399176;
MATHEMATICA
T[n_, k_]:= If[k==0, n!, If[k==1, n^(n-1), (1/n)*(k^(n+1)*n^n - n!*(k-1)*Sum[n^j*k^j/j!, {j, 0, n}])]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jan 06 2022 *)
PROG
(Sage)
@CachedFunction
def A137216(n, k):
if (k==0): return factorial(n)
elif (k==1): return n^(n-1)
else: return (1/n)*(k^(n+1)*n^n - factorial(n)*(k-1)*sum((n*k)^j/factorial(j) for j in (0..n)))
flatten([[A137216(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jan 06 2022
CROSSREFS
Sequence in context: A163493 A321405 A054200 * A369424 A070550 A298179
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 06 2008
EXTENSIONS
Edited by G. C. Greubel, Jan 06 2022
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)