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 A141417 (-1)^(n+1)*A091137(n)*a(0,n), where a(i,j) = Integral_{x=i..i+1} x*(x-1)*(x-2)*...*(x-j+1)/j! dx. 13
 -1, 1, 1, 1, 19, 27, 863, 1375, 33953, 57281, 3250433, 5675265, 13695779093, 24466579093, 132282840127, 240208245823, 111956703448001, 205804074290625, 151711881512390095, 281550972898020815, 86560056264289860203, 161867055619224199787, 20953816286242674495191, 39427936010479474495191 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This is row i=0 of an array defined as T(i,j) = (-1)^(i+j+1)*A091137(j)*a(i,j), columns j >= 0, which starts -1, 1, 1, 1, 19, 27, 863, ... 1, -3, 5, 1, 11, 11, 271, ... -1, 5, -23, 9, 19, 11, 191, ... 1, -7, 53, -55, 251, 27, 271, ... -1, 9, -95, 161, -1901, 475, 863, ... 1, -11, 149, -351, 6731, -4277, 19087, ... ... The first two rows are related via T(0,j) = A027760(j)*T(0,j-1) - T(1,j). REFERENCES P. Curtz, Integration .., note 12, C.C.S.A., Arcueil, 1969. LINKS FORMULA a(i,j) = a(i-1,j) + a(i-1,j-1), see reference page 33. (q+1-j)*Sum_{j=0..q} a(i,j)*(-1)^(q-j) = binomial(i,q), see reference page 35. a(n) = numerator(n*(n+1)*Sum_{k=1..n} ((-1)^(n-k)*Stirling2(n+k,k)*binomial(2*n-1,n-k))/((n+k)*(n+k-1))), n>0, a(0)=-1. - Vladimir Kruchinin, Dec 12 2016 MAPLE A091137 := proc(n) local a, i, p ; a := 1 ; for i from 1 do p := ithprime(i) ; if p > n+1 then break; fi; a := a*p^floor(n/(p-1)) ; od: a ; end proc: A048994 := proc(n, k) combinat[stirling1](n, k) ; end proc: a := proc(i, j) add(A048994(j, k)*x^k, k=0..j) ; int(%, x=i..i+1) ; %/j! ; end proc: A141417 := proc(n) (-1)^(n+1)*A091137(n)*a(0, n) ; end proc: seq(A141417(n), n=0..40) ; # R. J. Mathar, Nov 17 2010 MATHEMATICA (* a7 = A091137 *) a7[n_] := a7[n] = Times @@ Select[ Divisors[n]+1, PrimeQ]*a7[n-1]; a7[0]=1; a[n_] := (-1)^(n+1) * a7[n] * Integrate[ (-1)^n*Pochhammer[-x, n], {x, 0, 1}]/n!; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Aug 10 2012 *) PROG (Maxima) a(n):=if n=0 then -1 else num(n*(n+1)*sum(((-1)^(n-k)*stirling2(n+k, k)*binomial(2*n-1, n-k))/((n+k)*(n+k-1)), k, 1, n)); /* Vladimir Kruchinin, Dec 12 2016 */ CROSSREFS Cf. A141047, A140811, A140825. Sequence in context: A146651 A146808 A147232 * A264834 A069529 A138335 Adjacent sequences: A141414 A141415 A141416 * A141418 A141419 A141420 KEYWORD sign AUTHOR Paul Curtz, Aug 05 2008 EXTENSIONS Erroneous formula linking A091137 and A002196 removed, and more terms and program added by R. J. Mathar, Nov 17 2010 STATUS approved

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Last modified February 1 10:01 EST 2023. Contains 359992 sequences. (Running on oeis4.)