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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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