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URL: https://oeis.org/A142473

⇱ A142473 - OEIS

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A142473
Triangle T(n, k) = n! * StirlingS1(n, k)/binomial(n, k), read by rows.
1
1, -1, 2, 4, -6, 6, -36, 44, -36, 24, 576, -600, 420, -240, 120, -14400, 13152, -8100, 4080, -1800, 720, 518400, -423360, 233856, -105840, 42000, -15120, 5040, -25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320, 1625702400, -1104606720, 510295680, -193777920, 64653120, -19595520, 5503680, -1451520, 362880
OFFSET
1,3
COMMENTS
Row sums are: {1, 1, 4, -4, 276, -6348, 254976, -13188096, 887086080, ...}.
FORMULA
T(n, k) = n! * StirlingS1(n, k)/ binomial(n, k).
EXAMPLE
The triangle begins as:
1;
-1, 2;
4, -6, 6;
-36, 44, -36, 24;
576, -600, 420, -240, 120;
-14400, 13152, -8100, 4080, -1800, 720;
518400, -423360, 233856, -105840, 42000, -15120, 5040;
-25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320;
MAPLE
A142473:= (n, k)-> n!*Stirling1(n, k)/binomial(n, k);
seq(seq(A142473(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 02 2021
MATHEMATICA
T[n_, k_]:= n!*StirlingS1[n, k]/Binomial[n, k];
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 02 2021 *)
PROG
(Magma)
A142473:= func< n, k | Factorial(n)*StirlingFirst(n, k)/Binomial(n, k) >;
[A142473(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 02 2021
(SageMath)
def A142473(n, k): return (-1)^(n-k)*factorial(n)*stirling_number1(n, k)/binomial(n, k)
flatten([[A142473(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 02 2021
CROSSREFS
Cf. A008275.
Sequence in context: A383377 A225187 A281485 * A132426 A072646 A091476
KEYWORD
sign,tabl
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Apr 02 2021
STATUS
approved