cp's OEIS Frontend

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.

A049033 Central factorial numbers: unsigned 2nd subdiagonal of A182867.

This page as a plain text file.
%I A049033 #13 Jan 20 2025 06:40:11
%S A049033 1,56,4368,489280,75851776,15658639360,4165906530304,1390437378293760,
%T A049033 569462999991975936,280969831084430721024,164441704270786486861824,
%U A049033 112668650067303149573505024
%N A049033 Central factorial numbers: unsigned 2nd subdiagonal of A182867.
%D A049033 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
%F A049033 E.g.f.: (arcsin x)^6; that is, a_k is the coefficient of x^(2*k+6) in (arcsin x)^6 multiplied by (2*k+6)! and divided by 6!. - Joe Keane (jgk(AT)jgk.org)
%F A049033 (-1)^(n-2)*a(n-2) is the coefficient of x^5 in prod(k=0, 2*n, x+2*k-2*n). - _Benoit Cloitre_ and _Michael Somos_, Nov 22 2002
%e A049033 (arcsin x)^6 = x^6 + x^8 + 13/15*x^10 + 139/189*x^12 + ...
%p A049033 A049033 := proc(n)
%p A049033     arcsin(x)^6;
%p A049033     coeftayl(%,x=0,2*n+6)*(2*n+6)!/6! ;
%p A049033 end proc:
%p A049033 seq(A049033(n),n=0..20) ; # _R. J. Mathar_, Jan 20 2025
%Y A049033 Cf. A001824, A001825, A002455.
%Y A049033 Equals 4^n * A001820(n).
%K A049033 nonn
%O A049033 0,2
%A A049033 Joe Keane (jgk(AT)jgk.org)