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 A198628 Alternating sums of powers for 1,2,3,4 and 5. 4
 1, 3, 15, 81, 435, 2313, 12195, 63801, 331395, 1710153, 8775075, 44808921, 227890755, 1155180393, 5839846755, 29458152441, 148335904515, 745888593033, 3746364947235, 18799770158361, 94271405748675, 472449569948073, 2366624981836515, 11850654345690681, 59323452211439235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A196848 for the e.g.f.s and o.g.f.s of such sequences for the numbers 1,2,...,2*n+1, and A196847 for the numbers 1,2,...,2*n. LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120). FORMULA a(n) = sum(((-1)^(j+1))*j^n,j=1..5) = 1-2^n+3^n-4^n+5^n. E.g.f.: sum(((-1)^(j+1))*exp(j*x),j=1..5) = exp(x)*(1+exp(5*x))/(1+exp(x)). O.g.f.: sum(((-1)^(j+1))/(1-j*x),j=1..5) = (1-12*x+55*x^2-114*x^3+94*x^4)/product(1-j*x,j=1..5). A formula for the numbers of the numerator polynomial is given in A196848. MAPLE A198628 := proc(n) 3^n-4^n+1-2^n+5^n ; end proc: seq(A198628(n), n=0..20) ; # R. J. Mathar, May 11 2022 CROSSREFS Cf. A083323, A196847, A196848, A196837. Sequence in context: A253774 A003448 A229841 * A233020 A246020 A084120 Adjacent sequences: A198625 A198626 A198627 * A198629 A198630 A198631 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 27 2011 STATUS approved

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Last modified May 30 03:43 EDT 2023. Contains 363044 sequences. (Running on oeis4.)