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 A160562 Triangle of scaled central factorial numbers, T(n,k) = A008958(n,n-k). 4
 1, 1, 1, 1, 10, 1, 1, 91, 35, 1, 1, 820, 966, 84, 1, 1, 7381, 24970, 5082, 165, 1, 1, 66430, 631631, 273988, 18447, 286, 1, 1, 597871, 15857205, 14057043, 1768195, 53053, 455, 1, 1, 5380840, 397027996, 704652312, 157280838, 8187608, 129948, 680, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This is table 4 on page 12 of Gelineau and Zeng, read downwards by columns. If columns are read in the opposite direction, we get A008958. Apparently the table can also be obtained by deleting each second row and column of A136630. LINKS Yoann Gelineau and Jiang Zeng, Combinatorial Interpretations of the Jacobi-Stirling Numbers, arXiv:0905.2899 [math.CO], May 18 2009. FORMULA T(n,k) = (Sum_{m=0..k} (-1)^(k-m)*A039599(k,m)*(2*m+1)^(2*n))/(2*k)!/4^k. - Werner Schulte, Nov 01 2015 EXAMPLE Triangle starts: 1; 1, 1; 1, 10, 1; 1, 91, 35, 1; 1, 820, 966, 84, 1; ... MAPLE A160562 := proc(n, k) npr := 2*n+1 ; kpr := 2*k+1 ; sinh(t*sinh(x)) ; npr!*coeftayl(%, x=0, npr) ; coeftayl(%, t=0, kpr) ; end: seq(seq(A160562(n, k), k=0..n), n=0..15) ; # R. J. Mathar, Sep 09 2009 MATHEMATICA T[n_, k_] := Sum[(-1)^(k - m)*(2m + 1)^(2n + 1)*Binomial[2k, k + m]/(k + m + 1), {m, 0, k}]/(4^k*(2k)!); Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 22 2017 *) CROSSREFS Cf. A001819, A008275, A008277, A008958, A039599, A136630. Sequence in context: A129274 A176021 A166972 * A176243 A022173 A158117 Adjacent sequences:  A160559 A160560 A160561 * A160563 A160564 A160565 KEYWORD nonn,tabl AUTHOR Jonathan Vos Post, May 19 2009 EXTENSIONS More terms from R. J. Mathar, Sep 09 2009 STATUS approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)