A322127 -id:A322127 - cp's OEIS frontend

A322128 Triangular array, read by rows: T(n,k) = denominator of binomial(n-1, n-k)/k!, 1 <= k <= n.

1, 1, 2, 1, 1, 6, 1, 2, 2, 24, 1, 1, 1, 6, 120, 1, 2, 3, 12, 24, 720, 1, 1, 2, 6, 8, 120, 5040, 1, 2, 2, 24, 24, 240, 720, 40320, 1, 1, 3, 3, 12, 90, 180, 5040, 362880, 1, 2, 1, 2, 20, 40, 60, 1120, 40320, 3628800, 1, 1, 2, 1, 4, 20, 24, 336, 8064, 362880, 39916800

Offset: 1

Seiichi Manyama, Nov 27 2018

			See A322127.

Seiichi Manyama, Rows n = 1..140, flattened

Cf. A007318, A322093, A322127.

T[n_, k_] := Denominator[Binomial[n-1, n-k]/k!]; Table[T[n, k], {n,1,10}, {k,1,n}] // Flatten (* Amiram Eldar, Nov 27 2018 *)

A321382 Number of permutations of 6 copies of 1..n with no element equal to another within a distance of 1.

Original entry on oeis.org

1, 0, 2, 48852, 8437796016, 5752866855116280, 12229789732207993835280, 68139526686950961449783790480, 873795428893219442649940388795690880, 23337489207354946577030915302871598795308160

Offset: 0

Seiichi Manyama, Nov 28 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..91

Row 6 of A322093.

Cf. A190835, A322127, A322128.

a(n) = n! * A190835(n).

a(n) = Integral_{0..infinity} (Sum_{k=1..6} (-1)^(6-k) * binomial(5, 6-k) * x^k/k!)^n * exp(-x) dx.

A322095 Number of permutations of 7 copies of 1..n with no element equal to another within a distance of 1.

Original entry on oeis.org

1, 0, 2, 339720, 549023310936, 4383995385521886720, 131828993822765959468851600, 12202002913678756821228939869239920, 2988325485815656468293009880545684170044800, 1723427149081248135793318785599849462668815779427840

Offset: 0

Seiichi Manyama, Nov 28 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..80

Row 7 of A322093.

Cf. A190836, A322127, A322128.

a(n) = n! * A190836(n).

a(n) = Integral_{0..infinity} (Sum_{k=1..7} (-1)^(7-k) * binomial(6, 7-k) * x^k/k!)^n * exp(-x) dx.

A322096 Number of permutations of 8 copies of 1..n with no element equal to another within a distance of 1.

Original entry on oeis.org

1, 0, 2, 2403588, 36734931452736, 3470403228952634903280, 1490944857678655357195402606800, 2315418264816304038508896461231618573280, 10937192762438008527903830198163831816546577931520

Offset: 0

Seiichi Manyama, Nov 28 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..71

Row 8 of A322093.

Cf. A190837, A322127, A322128.

a(n) = n! * A190837(n).

a(n) = Integral_{0..infinity} (Sum_{k=1..8} (-1)^(8-k) * binomial(7, 8-k) * x^k/k!)^n * exp(-x) dx.

A322126 Number of permutations of the multiset {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,...,n,n,n,n,n} with no two consecutive terms equal.

Original entry on oeis.org

1, 0, 2, 7188, 134631576, 7946203275000, 1210527140790855600, 411490045733601418421040, 280031356887267221923677137280, 351026687723982522494728236869341440, 758933713536173718404757245269681913222400

Offset: 0

Seiichi Manyama, Nov 27 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..106

Row 5 of A322093.

Cf. A190833, A322127, A322128.

a[n_] := Integrate[(x - 2 * x^2 + x^3 - 1/6 * x^4 + 1/120 * x^5)^n * Exp[-x],  {x, 0, Infinity}]; Array[a, 10, 0] (* Stefano Spezia, Nov 27 2018 *)

a(n) = n! * A190833(n).

a(n) = Integral_{0..infinity} (x - 2 * x^2 + x^3 - 1/6 * x^4 + 1/120 * x^5)^n * exp(-x) dx.

A322145 Number of permutations of 9 copies of 1..n with no element equal to another within a distance of 1.

Original entry on oeis.org

1, 0, 2, 17236524, 2511603532825176, 2829059722872229922701920, 17498057808683351584656839871450000, 459422439054082909311010463927575656038701920, 42176005899746902650961357272521722186133207293858938240

Offset: 0

Seiichi Manyama, Nov 28 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..64

Row 9 of A322093.

Cf. A321669, A322127, A322128.

a(n) = n! * A321669(n).

a(n) = Integral_{0..infinity} (Sum_{k=1..9} (-1)^(9-k) * binomial(8, 9-k) * x^k/k!)^n * exp(-x) dx.

A322146 Number of permutations of 10 copies of 1..n with no element equal to another within a distance of 1.

Original entry on oeis.org

1, 0, 2, 124948668, 174702663548149248, 2360719028641481267959955040, 211490077066069537208795610578715159120, 94446414948214202156311984061437135600678877848560

Offset: 0

Seiichi Manyama, Nov 28 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..59

Row 10 of A322093.

Cf. A321670, A322127, A322128.

a(n) = n! * A321670(n).

a(n) = Integral_{0..infinity} (Sum_{k=1..10} (-1)^(10-k) * binomial(9, 10-k) * x^k/k!)^n * exp(-x) dx.

cp's OEIS Frontend

A322128 Triangular array, read by rows: T(n,k) = denominator of binomial(n-1, n-k)/k!, 1 <= k <= n.

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A321382 Number of permutations of 6 copies of 1..n with no element equal to another within a distance of 1.

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A322095 Number of permutations of 7 copies of 1..n with no element equal to another within a distance of 1.

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A322096 Number of permutations of 8 copies of 1..n with no element equal to another within a distance of 1.

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A322126 Number of permutations of the multiset {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,...,n,n,n,n,n} with no two consecutive terms equal.

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A322145 Number of permutations of 9 copies of 1..n with no element equal to another within a distance of 1.

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Formula

A322146 Number of permutations of 10 copies of 1..n with no element equal to another within a distance of 1.

Views

Author

Keywords

Links

Crossrefs

Formula