A001757 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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