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 A198630 Alternating sums of powers of 1,2,...,7. 1
 1, 4, 28, 208, 1540, 11344, 83188, 607408, 4416580, 31986064, 230784148, 1659338608, 11892395620, 84983496784, 605698755508, 4306834677808, 30560156566660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For the e.g.f.s and o.g.f.s of such alternating power sums see A196847 (even case) and A196848 (odd case). LINKS Table of n, a(n) for n=0..16. Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040). FORMULA a(n)=sum(((-1)^(j+1))*j^n,j=1..7), n>=0. E.g.f.: sum(((-1)^(j+1))*exp(j*x),j=1..7)= exp(x)* (1+exp(7*x))/(1+exp(x)). O.g.f: sum(((-1)^(j+1))/(1-j*x),j=1..7) = (1-24*x+238*x^2-1248*x^3+3661*x^4-5736*x^5+3828*x^6)/ product(1-j*x,j=1..7). See A196848 for a formula for the coefficients of the numerator polynomial. EXAMPLE a(2) = 1^2-2^2+3^2-4^2+5^2-6^2+7^2 = 28. MAPLE A198630 := proc(n) 3^n-4^n+1-2^n+5^n-6^n+7^n ; end proc: seq(A198630(n), n=0..20) ; # R. J. Mathar, May 11 2022 PROG (PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 5040, -13068, 13132, -6769, 1960, -322, 28]^n*[1; 4; 28; 208; 1540; 11344; 83188])[1, 1] \\ Charles R Greathouse IV, Jul 06 2017 CROSSREFS Cf. A000225, A083323, 2*A053154, A198628, 3*A198629. Sequence in context: A270471 A355354 A019482 * A246021 A090965 A106258 Adjacent sequences: A198627 A198628 A198629 * A198631 A198632 A198633 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 28 2011 STATUS approved

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Last modified June 7 21:29 EDT 2023. Contains 363157 sequences. (Running on oeis4.)