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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A374858 Obverse convolution (n)**(Lucas(n)); see Comments.

Original entry on oeis.org

2, 3, 24, 240, 4200, 110880, 4572288, 288812160, 28141344000, 4231979136000, 986721354178560, 357978242151129600, 202881784891968000000, 180248848162914585600000, 251851399750851061045248000, 554999919804958202694991872000, 1933790758313726593648946202624000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000027, A000032, A374848.

Programs

  • Mathematica
    s[n_] := n; t[n_] := LucasL[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

A374859 Obverse convolution (n)**(2^n); see Comments.

Original entry on oeis.org

1, 4, 36, 640, 21600, 1370880, 163924992, 37150064640, 16065713664000, 13343315521536000, 21404225432753602560, 66631099907380661452800, 404128087449517604339712000, 4791300434691082493755392000000, 111343541043408070030243833839616000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000027, A000079, A374848.

Programs

  • Mathematica
    s[n_] := n; t[n_] := 2^n;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

A374860 Obverse convolution (1)**A000201; see Comments.

Original entry on oeis.org

1, 2, 8, 40, 280, 2520, 25200, 302400, 3931200, 58968000, 1002456000, 18044208000, 360884160000, 7939451520000, 182607384960000, 4565184624000000, 118694800224000000, 3323454406272000000, 99703632188160000000, 3090812597832960000000, 101996815728487680000000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences. a(n+1)/a(n) is an integer for n>=0, so (a(n)) is a divisibility sequence.
A000201 is assumed to start with a(0) = 0.

Crossrefs

Cf. A000012, A000201, A001622, A374848, A026351.

Programs

  • Mathematica
    r = GoldenRatio;
s[n_] := 1; t[n_] := Floor[n*r];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

Formula

a(n) = Product_{k=0..n} A026351(k).

A374861 Obverse convolution (n)**A000201; see Comments.

Original entry on oeis.org

0, 1, 12, 144, 2400, 50400, 1143072, 31046400, 903260160, 30356726400, 1154305152000, 46189964620800, 2053748448460800, 100323076215398400, 5103635783178240000, 282151131740577792000, 16183501766885376000000, 999942682759884864000000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000027, A000201, A001622, A374848.

Programs

  • Mathematica
    r = GoldenRatio;
s[n_] := n; t[n_] := Floor[n*r];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 22}]

A374862 Obverse convolution A000201**A000201; see Comments.

Original entry on oeis.org

0, 1, 18, 256, 5400, 153664, 4251528, 146410000, 5159780352, 215051077696, 10497600000000, 516094438514944, 28802430771288192, 1806336000000000000, 113638807576776480768, 7916729578225695719424, 558793544769287109375000, 42995640737555012867053824
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences. a(2k+1) is a square for k>=0.

Crossrefs

Cf. A000201, A001622, A374848.

Programs

  • Mathematica
    r = GoldenRatio;
s[n_] := Floor[n*r];
u[n_] := Product[s[k] + s[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

A374863 Obverse convolution A000201**A001950; see Comments.

Original entry on oeis.org

0, 2, 45, 840, 23040, 823680, 29729700, 1319205888, 60949324800, 3307060721664, 207247208103936, 13289727219664896, 959973192342388224, 77222763982780416000, 6318019834620558704640, 568402264910884213555200, 52282854778694683852800000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.
A000201 and A001950 are assumed to start with a(0) = 0.

Crossrefs

Cf. A000201, A001950, A001622, A374848.

Programs

  • Mathematica
    r = GoldenRatio;
s[n_] := Floor[n*r]; t[n_] := Floor[n*r^2];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

A374864 Obverse convolution (1)**A001950; see Comments.

Original entry on oeis.org

1, 3, 18, 144, 1584, 22176, 354816, 6741504, 141571584, 3397718016, 91738386432, 2660413206528, 85133222608896, 2979662791311360, 110247523278520320, 4409900931140812800, 185215839107914137600, 8334712759856136192000, 400066212473094537216000
Offset: 0

Views

Author

Clark Kimberling, Aug 18 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences. a(n+1)/a(n) is an integer for n>=0, so (a(n)) is a divisibility sequence.

Crossrefs

Cf. A000012, A000201, A001622, A026352, A374848.

Programs

  • Mathematica
    r = GoldenRatio;
s[n_] := 1; t[n_] := Floor[n*r^2];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

Formula

a(n) = Product_{k=0..n} A026352(k).

A374865 Obverse convolution A000045**A000032; see Comments.

Original entry on oeis.org

2, 3, 18, 128, 2100, 61600, 3732480, 449880480, 111021510600, 55916730777600, 57813913372723200, 122742264040428032000, 535797463154791219200000, 4810427190599491339840000000, 88856328051357049141036014736800, 3377300175611111321142254817509376000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000032, A000045, A374848.

Programs

  • Mathematica
    s[n_] := Fibonacci[n]; t[n_] := LucasL[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

A374866 Obverse convolution (n)**(3n+2); see Comments.

Original entry on oeis.org

2, 15, 192, 3465, 80640, 2297295, 77414400, 3011753745, 132843110400, 6550564395375, 357082280755200, 21322087106945625, 1384050920207155200, 97036818423709539375, 7307788858693779456000, 588334230102950937230625, 50423743124987078246400000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000027, A016789, A374848.

Programs

  • Mathematica
    s[n_] := n; t[n_] := 3 n + 2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
(* or *)
Table[2^n*(n+2)*Pochhammer[2 + n/2, n], {n, 0, 20}] (* Vaclav Kotesovec, Aug 28 2024 *)

Formula

a(n) ~ 3^(3*(n+1)/2) * n^(n+1) / exp(n). - Vaclav Kotesovec, Aug 28 2024

A374867 Obverse convolution (2n+1)**A000045; see Comments.

Original entry on oeis.org

1, 6, 40, 504, 8640, 221760, 8087040, 426888000, 32620363776, 3648685824000, 602632706457600, 148439180079590400, 55016878371840000000, 30938118932878961836032, 26590262111772239462400000, 35154873540222607725345792000, 71898404594761985678156759040000
Offset: 0

Views

Author

Clark Kimberling, Aug 28 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A005408, A000045, A374848.

Programs

  • Mathematica
    s[n_] := 2 n + 1; t[n_] := Fibonacci[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
Previous Showing 21-30 of 58 results. Next

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