A001757 - OEIS

%I M1941 N0769 #29 Feb 01 2022 01:20:06

%S 1,1,2,9,54,450,4500,55125,771750,12502350,225042300,4538353050,

%T 99843767100,2410513805700,62673358948200,1762688220418125,

%U 52880646612543750,1698056319002793750,57733914846094987500,2084194325944029048750

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

%C For information about the trigonometric integral whose expansion involves the triangle A059366, see my comments and examples there. - _Petros Hadjicostas_, May 13 2020

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%F a(n) = A000984(floor(n/2))*A000984(ceiling(n/2))*A000142(n)/A000079(n). [Corrected by _Petros Hadjicostas_, May 13 2020]

%F From _Petros Hadjicostas_, May 13 2020: (Start)

%F a(n) = A059366(n, floor(n/2)) = A059366(n, ceiling(n/2)).

%F a(2*n) = A283678(n). (End)

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001

%E Corrected and extended by _Sean A. Irvine_, Nov 19 2012

%E a(0) = 1 prepended by _Petros Hadjicostas_, May 13 2020