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.

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A223514 Triangle T(n,k) represents the coefficients of (x^12*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Original entry on oeis.org

1, 12, 1, 276, 36, 1, 9384, 1536, 72, 1, 422280, 80040, 4920, 120, 1, 23647680, 4984560, 365400, 12000, 180, 1, 1584394560, 362597760, 30197160, 1205400, 24780, 252, 1, 123582775680, 30229617600, 2778370560, 127834560, 3237360, 45696, 336, 1, 1099867035520
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			1;
12,1;
276,36,1;
9384,1536,72,1;
422280,80040,4920,120,1;
23647680,4984560,365400,12000,180,1;
1584394560,362597760,30197160,1205400,24780,252,1;
123582775680,30229617600,2778370560,127834560,3237360,45696,336,1;
1099867035520,...

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^12*diff(b[j-1],x$1);
end do;

A223515 Triangle T(n,k) represents the coefficients of (x^13*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Original entry on oeis.org

1, 13, 1, 325, 39, 1, 12025, 1807, 78, 1, 589225, 102375, 5785, 130, 1, 35942725, 6936475, 466830, 14105, 195, 1, 2623818925, 549241875, 41948725, 1538810, 29120, 273, 1, 223024608625, 49858620175, 4198780950, 177364005, 4130490, 53690, 364, 1, 21633387036625
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			1;
13,1;
325,39,1;
12025,1807,78,1;
589225,102375,5785,130,1;
35942725,6936475,466830,14105,195,1
2623818925,549241875,41948725,1538810,29120,273,1;
223024608625,49858620175,4198780950,177364005,4130490,53690,364,1;
21633387036625,...

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^13*diff(b[j-1],x$1);
end do;

A223516 Triangle T(n,k) represents the coefficients of (x^14*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Original entry on oeis.org

1, 14, 1, 378, 42, 1, 15120, 2100, 84, 1, 801360, 128520, 6720, 140, 1, 52889760, 9412200, 585480, 16380, 210, 1, 4178291040, 805865760, 56836080, 1928640, 33810, 294, 1, 384402775680, 79123806720, 6148457280, 240056880, 5174400, 62328, 392, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			1;
14,1;
378,42,1;
15120,2100,84,1;
801360,128520,6720,140,1;
52889760,9412200,585480,16380,210,1;
4178291040,805865760,56836080,1928640,33810,294,1;
384402775680,79123806720,6148457280,240056880,5174400,62328,392,1;

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^14*diff(b[j-1],x$1);
end do;

A223517 Triangle T(n,k) represents the coefficients of (x^15*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Original entry on oeis.org

1, 15, 1, 435, 45, 1, 18705, 2415, 90, 1, 1066185, 158775, 7725, 150, 1, 75699135, 12497985, 722700, 18825, 225, 1, 6434426475, 1150525845, 75372885, 2379300, 38850, 315, 1, 637008221025, 121487010975, 8763187230, 318061485, 6380850, 71610, 420, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			1;
15,1;
435,45,1;
18705,2415,90,1;
1066185,158775,7725,150,1;
75699135,12497985,722700,18825,225,1;
6434426475,1150525845,75372885,2379300,38850,315,1;
637008221025,121487010975,8763187230,318061485,6380850,71610,420,1;

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^15*diff(b[j-1],x$1);
end do;

A223518 Triangle T(n,k) represents the coefficients of (x^16*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Original entry on oeis.org

1, 16, 1, 496, 48, 1, 22816, 2752, 96, 1, 1391776, 193440, 8800, 160, 1, 105774976, 16286656, 879840, 21440, 240, 1, 9625522816, 1604147328, 98111776, 2895200, 44240, 336, 1, 1020305418496, 181269286912, 12200219136, 413688576, 7761600, 81536, 448, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			1;
16,1;
496,48,1;
22816,2752,96,1;
1391776,193440,8800,160,1;
105774976,16286656,879840,21440,240,1;
9625522816,1604147328,98111776,2895200,44240,336,1;
1020305418496,181269286912,12200219136,413688576,7761600,81536,448,1

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^16*diff(b[j-1],x$1);
end do;

A223519 Triangle T(n,k) represents the coefficients of (x^17*d/dx)^n, where n=1,2,3,...

Original entry on oeis.org

1, 17, 1, 561, 51, 1, 27489, 3111, 102, 1, 1786785, 232815, 9945, 170, 1, 144729585, 20877615, 1058250, 24225, 255, 1, 14038769745, 2190735855, 125644365, 3480750, 49980, 357, 1, 1586380981185, 263782657215, 16639837830, 529411365, 9328410, 92106, 476, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Comments

Generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Examples

			1;
17,1;
561,51,1;
27489,3111,102,1;
1786785,232815,9945,170,1;
144729585,20877615,1058250,24225,255,1;
14038769745,2190735855,125644365,3480750,49980,357,1;
1586380981185,263782657215,16639837830,529411365,9328410,92106,476,1;

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^17*diff(b[j-1],x$1);
end do;

A223520 Triangle T(n,k) represents the coefficients of (x^18*d/dx)^n, where n=1,2,3,....

Original entry on oeis.org

1, 18, 1, 630, 54, 1, 32760, 3492, 108, 1, 2260440, 277200, 11160, 180, 1, 194397840, 26376840, 1259280, 27180, 270, 1, 20022977520, 2937589200, 158601240, 4140360, 56070, 378, 1, 2402757302400, 375471270720, 22286940480, 667865520, 11093040, 103320, 504, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Comments

Generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Examples

			1;
18,1;
630,54,1;
32760,3492,108,1;
2260440,277200,11160,180,1;
194397840,26376840,1259280,27180,270,1;
20022977520,2937589200,158601240,4140360,56070,378,1;
2402757302400,375471270720,22286940480,667865520,11093040,103320,504,1

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^18*diff(b[j-1],x$1);
end do;

A223521 Triangle T(n,k) represents the coefficients of (x^19*d/dx)^n, where n=1,2,3,...

Original entry on oeis.org

1, 19, 1, 703, 57, 1, 38665, 3895, 114, 1, 2822545, 326895, 12445, 190, 1, 256851595, 32896885, 1484280, 30305, 285, 1, 27996823855, 3875508945, 197651965, 4878440, 62510, 399, 1, 3555596629585, 524061968815, 29372612430, 831849165, 13067250, 115178, 532, 1
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Comments

Generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

Examples

			1;
19,1;
703,57,1;
38665,3895,114,1;
2822545,326895,12445,190,1;
256851595,32896885,1484280,30305,285,1;
27996823855,3875508945,197651965,4878440,62510,399,1;
3555596629585,524061968815,29372612430,831849165,13067250,115178,532,1;

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^19*diff(b[j-1],x$1);
end do;

A223525 Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*d/dx)^n when n=1,3,5,...

Original entry on oeis.org

1, 4, 3, 4, 24, 9, 28, 252, 189, 27, 280, 3360, 3780, 1080, 81, 3640, 54600, 81900, 35100, 5265, 243, 1106560, 4979520, 5335200, 2134080, 369360, 27702, 729, 24344320, 127807680, 164324160, 82162080, 18960480, 2133054, 112266, 2187, 608608000
Offset: 1

Views

Author

Udita Katugampola, Mar 18 2013

Keywords

Examples

			Triangle begins:
1;
4, 3;
4, 24, 9;,
28, 252, 189, 27;
280, 3360, 3780, 1080, 81;
3640, 54600, 81900, 35100, 5265, 243;
1106560, 4979520, 5335200, 2134080, 369360, 27702, 729;
24344320, 127807680, 164324160, 82162080, 18960480, 2133054, 112266, 2187;

Links

Crossrefs

Odd rows of A223169.
Cf. A223168-A223172, A223511-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;

A223526 Triangle S(n,k) by rows: coefficients of 3^(n/2)*(x^(2/3)*d/dx)^n when n=0,2,4,6,...

Original entry on oeis.org

1, 1, 3, 4, 24, 9, 28, 252, 189, 27, 280, 3360, 3780, 1080, 81, 3640, 54600, 81900, 35100, 5265, 243, 58240, 1048320, 1965600, 1123200, 252720, 23328, 729, 1106560, 23237760, 52284960, 37346400, 11203920, 1551312, 96957, 2187, 24344320, 584263680, 1533692160
Offset: 1

Views

Author

Udita Katugampola, Mar 18 2013

Keywords

Examples

			Triangle begins:
1;
1, 3;
4, 24, 9;
28, 252, 189, 27;
280, 3360, 3780, 1080, 81;
3640, 54600, 81900, 35100, 5265, 243;
58240, 1048320, 1965600, 1123200, 252720, 23328, 729;
1106560, 23237760, 52284960, 37346400, 11203920, 1551312, 96957, 2187;
24344320, 584263680, 1533692160, 1314593280, 492972480, 91010304, 8532216, 384912, 6561;

Links

Crossrefs

Even row of A223169.
Cf. A223168-A223172, A223511-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j];
end do;

Formula

T(n,0) = A007559(n) and T(n,n) = A000244(n) for all n>=0
Previous Showing 11-20 of 25 results. Next

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