A369019 -id:A369019 - cp's OEIS frontend

A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)(k - 1)^(k - 1)n*(n - k + 1)^(n - k).

0, 0, 1, 0, 4, 4, 0, 27, 18, 36, 0, 256, 144, 192, 432, 0, 3125, 1600, 1800, 2700, 6400, 0, 46656, 22500, 23040, 29160, 46080, 112500, 0, 823543, 381024, 367500, 423360, 564480, 918750, 2286144, 0, 16777216, 7529536, 6967296, 7560000, 9175040, 12600000, 20901888, 52706752

Offset: 0

Peter Luschny, Jan 13 2024

			Triangle read by rows:
[0] [0]
[1] [0,      1]
[2] [0,      4,      4]
[3] [0,     27,     18,     36]
[4] [0,    256,    144,    192,    432]
[5] [0,   3125,   1600,   1800,   2700,   6400]
[6] [0,  46656,  22500,  23040,  29160,  46080, 112500]
[7] [0, 823543, 381024, 367500, 423360, 564480, 918750, 2286144]

Cf. A369019, A368849.

T := (n, k) -> binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k):
seq(seq(T(n, k), k = 0..n), n=0..9);

A369018[n_, k_] := Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] n (n-k+1)^(n-k);
Table[A369018[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 27 2024 *)

def A369018(n, k):
    return binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k)

T = A368849 + A369019.

A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)(k - 1)^(k - 1)k*(n - k + 1)^(n - k).

Original entry on oeis.org

0, 1, 6, 57, 712, 10905, 197136, 4102777, 96552576, 2534382513, 73397843200, 2324613341721, 79923267523584, 2964436169152393, 117986961509824512, 5015721009078977625, 226816401312675168256, 10871698383944129824353, 550571805478900954497024

Offset: 0

Peter Luschny, Jan 13 2024

nonn

Cf. Row sums of A369019.

A369071 := n -> local k; add(binomial(n, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k), k=0..n): seq(A369071(n), n = 0..18);

A369071[n_] := Sum[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k), {k, n}]; Array[A369071, 20, 0] (* Paolo Xausa, Jan 28 2024 *)

def A369071(n):
    return sum(binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k)
           for k in range(n + 1))
print([A369071(n) for n in range(11)])

cp's OEIS Frontend

A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)(k - 1)^(k - 1)n*(n - k + 1)^(n - k).

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A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)(k - 1)^(k - 1)k*(n - k + 1)^(n - k).

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cp's OEIS Frontend

A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k).

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

SageMath

Formula

A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

SageMath

A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)(k - 1)^(k - 1)n*(n - k + 1)^(n - k).

A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)(k - 1)^(k - 1)k*(n - k + 1)^(n - k).