cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A039805 Matrix cube of partition triangle A008284.

Original entry on oeis.org

1, 3, 1, 6, 3, 1, 13, 9, 3, 1, 23, 19, 9, 3, 1, 44, 42, 22, 9, 3, 1, 74, 80, 48, 22, 9, 3, 1, 129, 154, 99, 51, 22, 9, 3, 1, 210, 273, 193, 105, 51, 22, 9, 3, 1, 345, 484, 362, 212, 108, 51, 22, 9, 3, 1, 542, 815, 651, 401, 218, 108, 51, 22, 9, 3, 1, 858, 1369, 1147
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

Row sums form A022812 (number of terms in n-th derivative of a function composed with itself 4 times). - Paul D. Hanna, Jul 13 2004

Examples

			1; 3,1; 6,3,1; 13,9,3,1; ...

Crossrefs

Cf. A038497, A038498, A039806, A039807. a(n, 1) = A022811(n) (first column).
Cf. A022812.

A022813 Number of terms in n-th derivative of a function composed with itself 5 times.

Original entry on oeis.org

1, 1, 5, 15, 45, 110, 271, 599, 1309, 2690, 5436, 10545, 20148, 37341, 68223, 121878, 214846, 371993, 636570, 1073325, 1790721, 2950922, 4816603, 7778937, 12455988, 19761148, 31108121, 48572686, 75307513, 115909727, 177255526, 269294119, 406708721, 610593948
Offset: 0

Views

Author

Winston C. Yang (yang(AT)math.wisc.edu)

Keywords

References

  • W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.

Links

Crossrefs

Cf. A008778, A022811-A022818, A024207-A024210. First column of A039807.

Programs

  • Mathematica
    b[n_, i_, k_] := b[n, i, k] = If[nJean-François Alcover, Apr 28 2017, after Alois P. Heinz *)

Formula

If a(n,m) = number of terms in m-derivative of a function composed with itself n times, p(n,k) = number of partitions of n into k parts, then a(n,m) = sum_{i=0..m} p(m,i)*a(n-1,i).

A050304 Matrix 10th power of partition triangle A008284.

Original entry on oeis.org

1, 10, 1, 55, 10, 1, 265, 65, 10, 1, 1045, 320, 65, 10, 1, 3817, 1365, 330, 65, 10, 1, 12583, 5127, 1420, 330, 65, 10, 1, 39148, 17710, 5447, 1430, 330, 65, 10, 1, 114235, 56638, 19030, 5502, 1430, 330, 65, 10, 1, 318857, 170993, 61865, 19350, 5512
Offset: 1

Views

Author

Christian G. Bower, Aug 15 1999

Keywords

Examples

			1; 10,1; 55,10,1; 265,65,10,1; ...

Crossrefs

Cf. A038497, A038498, A039805-A039807. A050300-A050303. a(n, 1) = A024210(n) (first column).

A050300 Matrix 6th power of partition triangle A008284.

Original entry on oeis.org

1, 6, 1, 21, 6, 1, 71, 27, 6, 1, 196, 92, 27, 6, 1, 532, 288, 98, 27, 6, 1, 1301, 799, 309, 98, 27, 6, 1, 3101, 2100, 891, 315, 98, 27, 6, 1, 6956, 5145, 2373, 912, 315, 98, 27, 6, 1, 15217, 12121, 5980, 2465, 918, 315, 98, 27, 6, 1, 31951, 27247, 14292, 6253
Offset: 1

Views

Author

Christian G. Bower, Aug 15 1999

Keywords

Examples

			1; 6,1; 21,6,1; 71,27,6,1; ...

Crossrefs

Cf. A038497, A038498, A039805-A039807. A050301-A050304. a(n, 1) = A022814(n) (first column).

A039806 Matrix 4th power of partition triangle A008284.

Original entry on oeis.org

1, 4, 1, 10, 4, 1, 26, 14, 4, 1, 55, 36, 14, 4, 1, 121, 91, 40, 14, 4, 1, 237, 202, 101, 40, 14, 4, 1, 468, 439, 238, 105, 40, 14, 4, 1, 867, 887, 524, 248, 105, 40, 14, 4, 1, 1597, 1758, 1105, 560, 252, 105, 40, 14, 4, 1, 2821, 3325, 2223, 1190, 570, 252, 105, 40
Offset: 0

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

Row sums form A022813 (number of terms in n-th derivative of a function composed with itself 5 times). - Paul D. Hanna, Jul 13 2004

Examples

			1; 4,1; 10,4,1; 26,14,4,1; ...

Crossrefs

Cf. A038497, A038498, A039805, A039807. a(n, 1) = A022812(n) (first column).
Cf. A022813.

A050301 Matrix 7th power of partition triangle A008284.

Original entry on oeis.org

1, 7, 1, 28, 7, 1, 105, 35, 7, 1, 322, 133, 35, 7, 1, 952, 455, 140, 35, 7, 1, 2541, 1379, 483, 140, 35, 7, 1, 6539, 3920, 1512, 490, 140, 35, 7, 1, 15833, 10375, 4354, 1540, 490, 140, 35, 7, 1, 37148, 26243, 11803, 4487, 1547, 490, 140, 35, 7, 1, 83594
Offset: 1

Views

Author

Christian G. Bower, Aug 15 1999

Keywords

Examples

			1; 7,1; 28,7,1; 105,35,7,1; ...

Crossrefs

Cf. A038497, A038498, A039805-A039807. A050300-A050304. a(n, 1) = A024207(n) (first column).

A050303 Matrix 9th power of partition triangle A008284.

Original entry on oeis.org

1, 9, 1, 45, 9, 1, 201, 54, 9, 1, 735, 246, 54, 9, 1, 2517, 981, 255, 54, 9, 1, 7785, 3453, 1026, 255, 54, 9, 1, 22857, 11238, 3699, 1035, 255, 54, 9, 1, 63024, 33930, 12183, 3744, 1035, 255, 54, 9, 1, 166819, 97038, 37464, 12429, 3753, 1035, 255, 54, 9, 1
Offset: 1

Views

Author

Christian G. Bower, Aug 15 1999

Keywords

Examples

			1; 9,1; 45,9,1; 201,54,9,1; ...

Crossrefs

Cf. A038497, A038498, A039805-A039807. A050300-A050304. a(n, 1) = A024209(n) (first column).

A050302 Matrix 8th power of partition triangle A008284.

Original entry on oeis.org

1, 8, 1, 36, 8, 1, 148, 44, 8, 1, 498, 184, 44, 8, 1, 1590, 682, 192, 44, 8, 1, 4586, 2236, 718, 192, 44, 8, 1, 12644, 6822, 2420, 726, 192, 44, 8, 1, 32775, 19346, 7476, 2456, 726, 192, 44, 8, 1, 81901, 52177, 21646, 7660, 2464, 726, 192, 44, 8, 1, 196085
Offset: 1

Views

Author

Christian G. Bower, Aug 15 1999

Keywords

Examples

			1; 8,1; 36,8,1; 148,44,8,1; ...

Crossrefs

Cf. A038497, A038498, A039805-A039807. A050301-A050304. a(n, 1) = A024208(n) (first column).
Showing 1-8 of 8 results.

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