A001757 Expansion of an integral: central elements of rows of triangle in A059366. (Formerly M1941 N0769)

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

Offset

0,3

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).

Links

Table of n, a(n) for n=0..19.

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)

Crossrefs

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

Sequence in context: A254795 A064151 A075679 * A267225 A078455 A366177

Adjacent sequences: A001754 A001755 A001756 * A001758 A001759 A001760

Keyword

nonn,easy

Author

N. J. A. Sloane

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

Status

approved