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.

Previous Showing 31-37 of 37 results.

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;

A223527 Triangle S(n,k) by rows: coefficients of 4^((n-1)/2)*(x^(1/4)*d/dx)^n when n=1,3,5,...

Original entry on oeis.org

1, 5, 4, 45, 72, 16, 585, 1404, 624, 64, 9945, 31824, 21216, 4352, 256, 208845, 835380, 742560, 228480, 26880, 1024, 5221125, 25061400, 27846000, 11424000, 2016000, 153600, 4096, 151412625, 847910700, 1130547600, 579768000, 136416000, 15590400, 831488, 16384
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			Triangle begins:
1;
5, 4;
45, 72, 16;
585, 1404, 624, 64;
9945, 31824, 21216, 4352, 256;
208845, 835380, 742560, 228480, 26880, 1024;
5221125, 25061400, 27846000, 11424000, 2016000, 153600, 4096;
151412625, 847910700, 1130547600, 579768000, 136416000, 15590400, 831488, 16384;

Links

Crossrefs

Odd rows of A223170.
Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(4^((i+1)mod 2)*x^((2((i+1)mod 2)+1)/4)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;

A223528 Triangle S(n,k) by rows: coefficients of 4^(n/2)*(x^(3/4)*d/dx)^n when n=0,2,4,6,...

Original entry on oeis.org

1, 1, 4, 5, 40, 16, 45, 540, 432, 64, 585, 9360, 11232, 3328, 256, 9945, 198900, 318240, 141440, 21760, 1024, 208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096, 5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384, 151412625
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			Triangle begins:
1;
1, 4;
5, 40, 16;
45, 540, 432, 64;
585, 9360, 11232, 3328, 256;
9945, 198900, 318240, 141440, 21760, 1024;
208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096;
5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384;
151412625, 4845204000, 13566571200, 12059174400, 4638144000, 873062400, 83148800, 3801088, 65536;

Links

Crossrefs

Even rows of A223170.
Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(4^((i+1)mod 2)*x^((2((i+1)mod 2)+1)/4)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j];
end do;

A223529 Triangle S(n,k) by rows: coefficients of 5^((n-1)/2)*(x^(1/5)*d/dx)^n when n=1,3,5,...

Original entry on oeis.org

1, 6, 5, 66, 110, 25, 1056, 2640, 1200, 125, 22176, 73920, 50400, 10500, 625, 576576, 2402400, 2184000, 682500, 81250, 3125, 17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625, 643458816, 3753509760, 5118422400, 2665845000, 634725000
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			Triangle begins:
1;
6, 5;
66, 110, 25;
1056, 2640, 1200, 125;
22176, 73920, 50400, 10500, 625;
576576, 2402400, 2184000, 682500, 81250, 3125;
17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;
643458816, 3753509760, 5118422400, 2665845000, 634725000, 73237500, 3937500, 78125;

Links

Crossrefs

Odd rows of A223171.
Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;

A223530 Triangle S(n,k) by rows: coefficients of 5^(n/2)*(x^(4/5)*d/dx)^n when n=0,2,4,6,...

Original entry on oeis.org

1, 1, 5, 6, 60, 25, 66, 990, 825, 125, 1056, 21120, 26400, 8000, 625, 22176, 554400, 924000, 420000, 65625, 3125, 576576, 17297280, 36036000, 21840000, 5118750, 487500, 15625, 17873856, 625584960, 1563962400, 1184820000, 370256250, 52893750, 3390625, 78125
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			Triangle begins:
1;
1, 5;
6, 60, 25;
66, 990, 825, 125;
1056, 21120, 26400, 8000, 625;
22176, 554400, 924000, 420000, 65625, 3125;
576576, 17297280, 36036000, 21840000, 5118750, 487500, 15625;
17873856, 625584960, 1563962400, 1184820000, 370256250, 52893750, 3390625, 78125;

Links

Crossrefs

Even rows of A223171.
Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j];
end do;

A223531 Triangle S(n,k) by rows: coefficients of 6^((n-1)/2)*(x^(1/6)*d/dx)^n when n=1,3,5,...

Original entry on oeis.org

1, 7, 6, 91, 156, 36, 1729, 4446, 2052, 216, 43225, 148200, 102600, 21600, 1296, 1339975, 5742750, 5301000, 1674000, 200880, 7776, 49579075, 254978100, 294205500, 123876000, 22297680, 1726272, 46656, 2131900225, 12791401350, 17711171100, 9321669000
Offset: 1

Views

Author

Udita Katugampola, Mar 23 2013

Keywords

Examples

			Triangle begins:
1;
7, 6;
91, 156, 36;
1729, 4446, 2052, 216;
43225, 148200, 102600, 21600, 1296;
1339975, 5742750, 5301000, 1674000, 200880, 7776;
49579075, 254978100, 294205500, 123876000, 22297680, 1726272, 46656;
2131900225, 12791401350, 17711171100, 9321669000, 2237200560, 259803936, 14043456, 279936;

Links

Crossrefs

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

Programs

  • Maple
    a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(6^((i+1)mod 2)*x^((4((i+1)mod 2)+1)/6)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;
Previous Showing 31-37 of 37 results.

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