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 A185690 Exponential Riordan array (1,sin(x)). 2
 1, 0, 1, -1, 0, 1, 0, -4, 0, 1, 1, 0, -10, 0, 1, 0, 16, 0, -20, 0, 1, -1, 0, 91, 0, -35, 0, 1, 0, -64, 0, 336, 0, -56, 0, 1, 1, 0, -820, 0, 966, 0, -84, 0, 1, 0, 256, 0, -5440, 0, 2352, 0, -120, 0, 1, -1, 0, 7381, 0, -24970, 0, 5082, 0, -165, 0, 1, 0, -1024, 0, 87296, 0, -90112, 0, 10032, 0, -220, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS The row n=0 with T(0,0)=1 and the column T(n,0)=0, n>0, are not entered into the sequence here. A signed version of A136630 (apart from row 0 and column 0). - Peter Bala, Oct 06 2011 LINKS Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 FORMULA T(n,k)= 2^(1-k)/k! *sum{i=0..floor(k/2)} (-1)^(floor((n+k)/2)-i) *binomial(k,i) *(2*i-k)^n, for even(n-k). EXAMPLE 1; 0,1; -1,0,1; 0,-4,0,1; 1,0,-10,0,1; 0,16,0,-20,0,1; -1,0,91,0,-35,0,1; 0,-64,0,336,0,-56,0,1; MAPLE A185690 := proc(n, k) if type(k+n, 'even') then 2^(1-k)/k! * add( (-1)^(floor((n+k)/2)-i)*binomial(k, i)*(2*i-k)^n, i=0..floor(k/2)) ; else 0; end if; end proc: # R. J. Mathar, Feb 21 2011 MATHEMATICA t[n_, k_] /; OddQ[n - k] = 0; t[n_, k_] /; EvenQ[n - k] := 2^(1-k)/k!* Sum[ (-1)^(Floor[(n+k)/2] - i)*Binomial[k, i]*(2*i-k)^n, {i, 0, k/2}]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 21 2013 *) CROSSREFS Cf. A136630. Sequence in context: A006838 A061309 A059064 * A096459 A218453 A186372 Adjacent sequences:  A185687 A185688 A185689 * A185691 A185692 A185693 KEYWORD sign,tabl AUTHOR Vladimir Kruchinin, Feb 10 2011 STATUS approved

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