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 A300437 Triangle T(nu,m) read by rows: The number of N-color odd self-inverse compositions of (2*nu+1) into (2*m+1) parts. 3
 1, 3, 1, 5, 3, 1, 7, 8, 3, 1, 9, 16, 11, 3, 1, 11, 29, 25, 14, 3, 1, 13, 47, 58, 34, 17, 3, 1, 15, 72, 110, 96, 43, 20, 3, 1, 17, 104, 206, 200, 143, 52, 23, 3, 1, 19, 145, 346, 442, 317, 199, 61, 26, 3, 1, 21, 195, 571, 822, 807, 461, 264, 70, 29, 3, 1, 23, 256, 881, 1565, 1613, 1328, 632, 338 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Table 1 of Guo contains several typos which are not compliant with the formula on page 4 for S_o(2k+1,2l+1). Also the formula has been modified to read S_o(2k+1,2l+1) = sum_{t=1..2k+1) sum_{i+j= (2k+1-t-2l)/4} t*binomial(2l+i-1,2l-1)*binomial(l,j). So the upper limit on t has been extended and a factor t has been inserted. LINKS Y.-h. Guo, n-Color Odd Self-Inverse Compositions, J. Int. Seq. 17 (2014) # 14.10.5, Table 1. FORMULA 64*T(nu+2,2) = 51 +1306/15*nu +13*(-1)^nu +56/3*nu^3 +170/3*nu^2 +4/15*nu^5 +10*(-1)^nu*nu +2*(-1)^nu*nu^2 +10/3*nu^4 with g.f. (1+x^2)^2/[(1+x)^3*(1-x)^6], column 2. EXAMPLE The triangle starts in row nu=0 with columns 0<=m<=nu as: 1; 3,1; 5,3,1; 7,8,3,1; 9,16,11,3,1; 11,29,25,14,3,1; 13,47,58,34,17,3,1; 15,72,110,96,43,20,3,1; 17,104,206,200,143,52,23,3,1; 19,145,346,442,317,199,61,26,3,1; 21,195,571,822,807,461,264,70,29,3,1; 23,256,881,1565,1613,1328,632,338,79,32,3,1; 25,328,1337,2671,3478,2800,2032,830,421,88,35,3,1; 27,413,1939,4596,6402,6742,4464,2946,1055,513,97,38,3,1; MAPLE A300437 := proc(k, l)     local a, t, i, j ;     a := 0 ;     for t from 1 to 2*k+1 by 2 do         for j from 0 to l do             i := (2*k+1-t-2*l)/4-j ;             if type(i, 'integer') then                 a := a+t*binomial(2*l+i-1, 2*l-1)*binomial(l, j) ;             end if;         end do:     end do:     a ; end proc: seq(seq(A300437(k, l), l=0..k), k=0..13) ; CROSSREFS Cf. A131941 (column 2?), A300438 (row sums), A292835. Sequence in context: A133601 A258207 A133094 * A208607 A159291 A122510 Adjacent sequences:  A300434 A300435 A300436 * A300438 A300439 A300440 KEYWORD nonn,tabl,easy AUTHOR R. J. Mathar, Mar 05 2018 STATUS approved

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Last modified June 19 12:50 EDT 2021. Contains 345129 sequences. (Running on oeis4.)