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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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A001757 Expansion of an integral: central elements of rows of triangle in A059366.

Original entry on oeis.org

1, 1, 2, 9, 54, 450, 4500, 55125, 771750, 12502350, 225042300, 4538353050, 99843767100, 2410513805700, 62673358948200, 1762688220418125, 52880646612543750, 1698056319002793750, 57733914846094987500, 2084194325944029048750
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

For information about the trigonometric integral whose expansion involves the triangle A059366, see my comments and examples there. - Petros Hadjicostas, May 13 2020

References

  • L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A000079, A000142, A000984, A059366, A283678.

Formula

a(n) = A000984(floor(n/2))*A000984(ceiling(n/2))*A000142(n)/A000079(n). [Corrected by Petros Hadjicostas, May 13 2020]
From Petros Hadjicostas, May 13 2020: (Start)
a(n) = A059366(n, floor(n/2)) = A059366(n, ceiling(n/2)).
a(2*n) = A283678(n). (End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001
Corrected and extended by Sean A. Irvine, Nov 19 2012
a(0) = 1 prepended by Petros Hadjicostas, May 13 2020
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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