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 1-10 of 27 results. Next

A029609 Central numbers in the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

1, 5, 15, 50, 175, 630, 2310, 8580, 32175, 121550, 461890, 1763580, 6760390, 26001500, 100291500, 387793800, 1502700975, 5834015550, 22687838250, 88363159500, 344616322050, 1345644686100, 5260247409300, 20583576819000, 80619009207750, 316026516094380, 1239796332370260
Offset: 0

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Author

Mohammad K. Azarian

Keywords

Comments

For n > 0 also central terms of (1,4)-Pascal triangle A095666. - Reinhard Zumkeller, Apr 08 2012

Links

Crossrefs

Cf. A000108, A029600, A095666.

Programs

  • Haskell
    a029609 n = a029600 (2*n) n  -- Reinhard Zumkeller, Apr 08 2012
  • Mathematica
    a[n_]=(5*Binomial[2*n,n]-3KroneckerDelta[n,0])/2; Array[a,27,0] (* Stefano Spezia, Feb 14 2025 *)

Formula

From Peter Bala, Aug 16 2011: (Start)
a(n) = (5/2)*binomial(2*n,n) for n >= 1.
O.g.f.: -3/2+5/2*1/sqrt(1-4*x) = 1+5*x+15*x^2+50*x^3+... = 1+5*x*d/dx(log(C(x))), where C(x) is the o.g.f. for the Catalan numbers A000108. (End)
E.g.f.: (5*exp(2*x)*BesselI(0, 2*x) - 3)/2. - Stefano Spezia, Feb 14 2025

Extensions

More terms from James Sellers

A029605 Even numbers in the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

2, 2, 2, 8, 2, 2, 24, 26, 14, 2, 50, 40, 2, 48, 90, 20, 2, 2, 80, 196, 308, 322, 224, 100, 26, 2, 276, 504, 630, 546, 324, 126, 2, 120, 780, 1134, 1176, 870, 450, 32, 2, 1914, 2310, 2046, 1320, 2, 168, 638, 1650, 4224, 4356, 3366, 792, 222, 38, 2, 806, 2288, 8580
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029607 Even numbers in the (2,3)-Pascal triangle A029600 that are different from 2.

Original entry on oeis.org

8, 24, 26, 14, 50, 40, 48, 90, 20, 80, 196, 308, 322, 224, 100, 26, 276, 504, 630, 546, 324, 126, 120, 780, 1134, 1176, 870, 450, 32, 1914, 2310, 2046, 1320, 168, 638, 1650, 4224, 4356, 3366, 792, 222, 38, 806, 2288, 8580, 7722, 1014, 260, 224, 3094, 12012
Offset: 1

Views

Author

Mohammad K. Azarian

Keywords

Crossrefs

Cf. A029600.

Extensions

More terms from James Sellers

A029613 Even numbers (not equal to 2) to the left of the central elements of the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

24, 48, 80, 196, 308, 276, 504, 120, 780, 1134, 1914, 168, 638, 1650, 4224, 806, 2288, 224, 3094, 12012, 288, 1480, 5320, 14196, 29120, 46904, 60060, 1768, 6800, 19516, 43316, 76024, 106964, 360, 8568, 26316, 62832, 119340, 182988, 228514, 34884
Offset: 0

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Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029617 Table read by rows: list of even numbers to the right of the central elements of the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

8, 26, 14, 40, 90, 20, 322, 224, 100, 26, 546, 324, 126, 1176, 870, 450, 32, 2046, 1320, 4356, 3366, 792, 222, 38, 7722, 1014, 260, 16302, 8008, 1274, 44, 61490, 50336, 32760, 16744, 6580, 1920, 392, 50, 111826, 83096, 49504, 23324, 8500, 2312, 442
Offset: 0

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Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029601 Distinct numbers in the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 9, 15, 11, 24, 26, 14, 13, 35, 50, 40, 17, 48, 85, 90, 57, 20, 63, 133, 175, 147, 77, 23, 19, 80, 196, 308, 322, 224, 100, 21, 99, 276, 504, 630, 546, 324, 126, 29, 120, 375, 780, 1134, 1176, 870, 450, 155, 32, 25, 143, 495, 1155, 1914, 2310, 2046
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers, Dec 08 1999

A029602 Numbers in the (2,3)-Pascal triangle A029600 that are different from 2.

Original entry on oeis.org

1, 3, 5, 3, 7, 8, 3, 9, 15, 11, 3, 11, 24, 26, 14, 3, 13, 35, 50, 40, 17, 3, 15, 48, 85, 90, 57, 20, 3, 17, 63, 133, 175, 147, 77, 23, 3, 19, 80, 196, 308, 322, 224, 100, 26, 3, 21, 99, 276, 504, 630, 546, 324, 126, 29, 3, 23, 120, 375, 780, 1134, 1176, 870, 450, 155, 32
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029603 Numbers in the (2,3)-Pascal triangle A029600 that are different from 3.

Original entry on oeis.org

1, 2, 2, 5, 2, 7, 8, 2, 9, 15, 11, 2, 11, 24, 26, 14, 2, 13, 35, 50, 40, 17, 2, 15, 48, 85, 90, 57, 20, 2, 17, 63, 133, 175, 147, 77, 23, 2, 19, 80, 196, 308, 322, 224, 100, 26, 2, 21, 99, 276, 504, 630, 546, 324, 126, 29, 2, 23, 120, 375, 780, 1134, 1176, 870, 450, 155
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029604 Odd numbers in the (2,3)-Pascal triangle A029600.

Original entry on oeis.org

1, 3, 5, 3, 7, 3, 9, 15, 11, 3, 11, 3, 13, 35, 17, 3, 15, 85, 57, 3, 17, 63, 133, 175, 147, 77, 23, 3, 19, 3, 21, 99, 29, 3, 23, 375, 155, 3, 25, 143, 495, 1155, 605, 187, 35, 3, 27, 3069, 1925, 3, 29, 195, 4719, 7293, 5291, 2717, 41, 3, 31, 1001, 7007, 15873, 13013
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers

A029606 Odd numbers in the (2,3)-Pascal triangle A029600 that are different from 3.

Original entry on oeis.org

1, 5, 7, 9, 15, 11, 11, 13, 35, 17, 15, 85, 57, 17, 63, 133, 175, 147, 77, 23, 19, 21, 99, 29, 23, 375, 155, 25, 143, 495, 1155, 605, 187, 35, 27, 3069, 1925, 29, 195, 4719, 7293, 5291, 2717, 41, 31, 1001, 7007, 15873, 13013, 3731, 301, 33, 255, 1225, 4095
Offset: 0

Views

Author

Mohammad K. Azarian

Keywords

Extensions

More terms from James Sellers
Showing 1-10 of 27 results. Next

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