A178886 -id:A178886 - cp's OEIS frontend

A179972 Irregular table T(n,k) = A178886(n,k)/A048996(n,k) read by rows.

1, 1, 1, 2, 1, 1, 6, 2, 2, 1, 1, 24, 6, 6, 2, 2, 1, 1, 120, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 720, 120, 120, 120, 24, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 5040, 720, 720, 720, 720, 120, 120, 120, 120, 120, 24, 24, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 40320

Offset: 1

Alford Arnold, Aug 04 2010

Row n has A000041(n) terms.
Consider the five partitions of the number 4:
4 3+1 2+2 2+1+1 and 1+1+1+1
rewriting as 4000 3100 2200 2110 and 1111
then a(n) counts the ways that the zeros can be permuted:
6,2,2,1,1
agreeing with the factorial of the difference between A036042 and A036043.

			Row four of A178886 begins: 6 4 2 3 1
Row four of A048996 begins: 1 2 1 3 1
so,
Row four of A179972 begins: 6 2 2 1 1
Triangle T(n,k) begins:
    1;
    1,  1;
    2,  1,  1;
    6,  2,  2,  1, 1;
   24,  6,  6,  2, 2, 1, 1;
  120, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1;
  ...

Cf. A178886, A048996, A036042, A036043, A179973 (row sums).

T(n,k) = ( A036042(n,k) - A036043(n,k))!.

T(n,k) = n!/A178888(n,k). - R. J. Mathar, Mar 03 2011

A178883 Multiply, cell by cell, the sequences A096162, A048996 and A178886.

Original entry on oeis.org

1, 1, 2, 2, 4, 6, 6, 8, 4, 18, 24, 24, 24, 24, 36, 36, 96, 120, 120, 96, 96, 48, 108, 216, 36, 192, 288, 600, 720, 720, 480, 480, 480, 432, 864, 432, 432, 576, 1728, 576, 1200, 2400, 4320, 5040

Offset: 1

Alford Arnold, Jun 23 2010

Shape sequence for this irregular table is A000041.

			Row 3: (1,1,6) times (1,2,1) times (2,2,1) yielding (2,4,6) with row sum 12 agreeing with 1,3,12,60,360,...; cf. A001700.

Cf. A000041, A001700, A048996, A096162, A178886.

Cf. A162608, A001710 (row sums). - Alford Arnold, Sep 28 2010

More terms from Alford Arnold, Sep 28 2010

A179236 Irregular triangle T(n,k) = A096162(n,k)* A036040(n,k)* A048996(n,k)A098546(n,k) A178886(n,k) read by rows, 1<=k<=A000041(n).

Original entry on oeis.org

1, 2, 2, 6, 36, 6, 24, 192, 72, 432, 24, 120, 1200, 2400, 3600, 5400, 4800, 120, 720, 8640, 21600, 7200, 32400, 259200, 10800, 57600, 194400, 54000, 720, 5040, 70560, 211680, 352800, 317520, 3175200, 1058400, 1587600, 705600, 12700800, 2116800, 882000, 5292000, 635040, 5040, 40320, 645120, 2257920, 4515840

Offset: 1

Alford Arnold, Jul 04 2010

			The factor sequences begin
1..1..2..1..1..6
1..1..1..1..3..1
1..1..1..1..2..1
1..2..1..3..3..1
1..1..1..2..2..1
so the present sequence begins
1..2..2..6..36..6

Cf. A000041 (row lengths) A096161 A000110 A000079 A098545 A000522 A179235 (row sums)

cp's OEIS Frontend

A179972 Irregular table T(n,k) = A178886(n,k)/A048996(n,k) read by rows.

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Comments

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Formula

A178883 Multiply, cell by cell, the sequences A096162, A048996 and A178886.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A179236 Irregular triangle T(n,k) = A096162(n,k)* A036040(n,k)* A048996(n,k)A098546(n,k) A178886(n,k) read by rows, 1<=k<=A000041(n).

Views

Author

Keywords

Examples

Crossrefs

cp's OEIS Frontend

A179972 Irregular table T(n,k) = A178886(n,k)/A048996(n,k) read by rows.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A178883 Multiply, cell by cell, the sequences A096162, A048996 and A178886.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A179236 Irregular triangle T(n,k) = A096162(n,k)* A036040(n,k)* A048996(n,k)*A098546(n,k)* A178886(n,k) read by rows, 1<=k<=A000041(n).

Views

Author

Keywords

Examples

Crossrefs

A179236 Irregular triangle T(n,k) = A096162(n,k)* A036040(n,k)* A048996(n,k)A098546(n,k) A178886(n,k) read by rows, 1<=k<=A000041(n).