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 A185951 Exponential Riordan array (1, x*cosh(x)). 1
 1, 0, 1, 3, 0, 1, 0, 12, 0, 1, 5, 0, 30, 0, 1, 0, 120, 0, 60, 0, 1, 7, 0, 735, 0, 105, 0, 1, 0, 896, 0, 2800, 0, 168, 0, 1, 9, 0, 15372, 0, 8190, 0, 252, 0, 1, 0, 5760, 0, 114240, 0, 20160, 0, 360, 0, 1, 11, 0, 270765, 0, 556710, 0, 43890, 0, 495, 0, 1, 0, 33792, 0, 4118400, 0, 2084544, 0, 87120, 0, 660, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The column k=0 of the array (which contains T(0,0)=1 and otherwise zero) is not included in the triangle. Also the Bell transform of the sequence "a(n) = n+1 if n is even else 0". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2013. FORMULA T(n,k) = binomial(n,k)/(2^k) * Sum_{i=0..k} binomial(k,i) *(k-2*i)^(n-k), n > k; T(n,n) = 1. EXAMPLE Array begins 1, 0, 1, 3, 0, 1, 0, 12, 0, 1, 5, 0, 30, 0, 1, 0, 120, 0, 60, 0, 1, 7, 0, 735, 0, 105, 0, 1, 0, 896, 0, 2800, 0, 168, 0, 1, 9, 0, 15372, 0, 8190, 0, 252, 0, 1, 0, 5760, 0, 114240, 0, 20160, 0, 360, 0, 1, 11, 0, 270765, 0, 556710, 0, 43890, 0, 495, 0, 1, 0, 33792, 0, 4118400, 0, 2084544, 0, 87120, 0, 660, 0, 1. MAPLE A185951 := proc(n, k) if n =k then 1; else binomial(n, k)/2^k * add( binomial(k, i)*(k-2*i)^(n-k), i=0..k) ; end if; end proc: # R. J. Mathar, Feb 22 2011 # The function BellMatrix is defined in A264428. # Adds (1, 0, 0, 0, ..) as column 0. BellMatrix(n -> `if`(n::even, n+1, 0), 10); # Peter Luschny, Jan 29 2016 MATHEMATICA t[n_, k_] := Binomial[n, k]/(2^k)* Sum[ Binomial[k, i]*(k-2*i)^(n-k), {i, 0, k}]; t[n_, n_] = 1; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 14 2013, from formula *) BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]]; B = BellMatrix[Function[n, If[EvenQ[n], n + 1, 0]], rows = 12]; Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *) CROSSREFS Sequence in context: A132884 A319234 A210473 * A188832 A279514 A094675 Adjacent sequences: A185948 A185949 A185950 * A185952 A185953 A185954 KEYWORD nonn,tabl AUTHOR Vladimir Kruchinin, Feb 11 2011 STATUS approved

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Last modified May 18 16:32 EDT 2024. Contains 372664 sequences. (Running on oeis4.)