# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a230324 Showing 1-1 of 1 %I A230324 #22 Jan 19 2018 19:35:24 %S A230324 2,1,-1,-2,1,6,-3,-34,17,310,-155,-4146,2073,76454,-38227,-1859138, %T A230324 929569,57641238,-28820619,-2219305810,1109652905,103886563462, %U A230324 -51943281731,-5810302084962,2905151042481,382659344967926 %N A230324 a(n) = A226158(n) - 2*A226158(n+1). %C A230324 The array A(n,k) = A(n-1,k+1) - A(n-1,k) of the sequence in the first row and higher-order sequences in followup rows starts: %C A230324 2, 1, -1, -2, 1, 6, -3, ... %C A230324 -1, -2, -1, 3, 5, -9, -31, ... %C A230324 -1, 1, 4, 2, -14, -22, 82, ... %C A230324 2, 3, -2, -16, -8, 104, 160, ... %C A230324 1, -5, -14, 8, 112, 56, -1160, ... %C A230324 -6, -9, 22, 104, -56, -1216, -608, ... %C A230324 -3, 31, 82, -160, -1160, 608, 18880, ... %C A230324 etc. %C A230324 a(n) is an autosequence: Its inverse binomial transform is the sequence (up to a sign), which means top row and left column in the difference array have the same absolute values. %C A230324 The main diagonal is the double of the first upper diagonal: A(n,n) = 2*A(n,n+1). %C A230324 A(n,n+1) = (-1)^n*A005439(n), which also appears as the first upper diagonal of the difference array of A226158(n). %H A230324 G. C. Greubel, Table of n, a(n) for n = 0..500 %H A230324 OEIS Wiki, Autosequence %F A230324 a(n)/2 + A164555(n)/A027642(n) = 2*A225825(n)/A141056(n). %e A230324 a(0) = 0 - 2 * (-1) = 2, %e A230324 a(1) = -1 - 2 * (-1) = 1, %e A230324 a(2) = -1 - 2 * 0 = -1, %e A230324 a(3) = 0 - 2 * 1 = -2, %e A230324 a(4) = 1 - 2 * 0 = 1, %e A230324 a(5) = 0 - 2 * (-3) = 6. %p A230324 A226158 := proc(n) %p A230324 if n = 0 then %p A230324 0; %p A230324 else %p A230324 Zeta(1-n)*2*n*(2^n-1) ; %p A230324 end if; %p A230324 end proc: %p A230324 A230324 := proc(n) %p A230324 A226158(n)-2*A226158(n+1) ; %p A230324 end proc: # _R. J. Mathar_, Oct 28 2013 %t A230324 a[0] = 2; a[1] = 1; a[n_] := n EulerE[n-1, 0] - 2 (n+1) EulerE[n, 0]; %t A230324 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Jun 07 2017 *) %Y A230324 Cf. A050946. %K A230324 sign %O A230324 0,1 %A A230324 _Paul Curtz_, Oct 16 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE