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 A097301 Numerators of rationals used in the Euler-Maclaurin type derivation of Stirling's formula for N!. 2
 1, -1, 2, -3, 3360, -995040, 39916800, -656924748480, 1214047650816000, -169382556838010880, 15749593891765493760000, -4054844479616799289344000, 34017686450062663131463680000, -11402327189708082115897599590400000, 189528830020089532044244068728832000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Denominators are given in A097302. The e.g.f. sum( A(2*n+1)*(x^(2*n+1))/(2*n+1)!,n=0..infinity) appears in the Stirling-formula derivation for N! with x=1/N in the exponent and the formula for A(2*n+1):=a(n)/A097302(n), n>=0, is given below. For Stirling's formula see A001163 and A001164. The rationals A(2*n+1) = B(n):= (2*n)!*Bernoulli(2*(n+1))/(2*(n+1)) = a(n)/A097304(n) with A(2*n):=0 are the logarithmic transform of the rational sequence {A001163(n)/A001164(n)} (inverse of the sequence transform EXP) REFERENCES Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, p. 87. LINKS W. Lang, More terms and comments. N. J. A. Sloane, Transforms FORMULA a(n)=numerator(B(n)) with B(n):=Bernoulli(2*n+2)*(2*n)!/(2*n+2) and Bernoulli(n)= A027641(n)/A027642(n). CROSSREFS Sequence in context: A257552 A038104 A290972 * A020345 A341715 A085943 Adjacent sequences:  A097298 A097299 A097300 * A097302 A097303 A097304 KEYWORD sign,frac,easy AUTHOR Wolfdieter Lang, Aug 13 2004 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)