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 A269792 a(n) = 5*n^4. 2
 0, 5, 80, 405, 1280, 3125, 6480, 12005, 20480, 32805, 50000, 73205, 103680, 142805, 192080, 253125, 327680, 417605, 524880, 651605, 800000, 972405, 1171280, 1399205, 1658880, 1953125, 2284880, 2657205, 3073280, 3536405, 4050000, 4617605, 5242880, 5929605 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS More generally, the ordinary generating function for the sequences of the form k*n^m, is k*Sum_{j>=1}x^j*j^m (when abs(x)<1). More generally, the ordinary generating function for the values of quartic polynomial p*n^4 + q*n^3 + k*n^2 + m*n + r, is (r + (p + q + k + m - 4*r)*x + (11*p + 3*q - k - 3*m + 6*r)*x^2 + (11*p - 3*q - k + 3*m - 4*r)*x^3 + (p - q + k - m + r)*x^4)/(1 - x)^5. LINKS Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1) FORMULA G.f.: 5*x*(1 + 11*x + 11*x^2 + x^3)/(1 - x)^5. E.g.f.: 5*exp(x)^x*x*(1 + 7*x + 6*x^2 + x^3). a(n) = 5*a(n-1) - 10*(9n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). a(n) = 5*A000583(n) = A008587(n)*A000578(n). Sum_{n>=1} 1/a(n) = Pi^4/450 = (1/450)*A092425 = 0.216464646742... MAPLE A269792:=n->5*n^4: seq(A269792(n), n=0..50); # Wesley Ivan Hurt, Apr 28 2017 MATHEMATICA Table[5 n^4, {n, 0, 33}] LinearRecurrence[{5, -10, 10, -5, 1}, {0, 5, 80, 405, 1280}, 34] PROG (PARI) x='x+O('x^99); concat(0, Vec(5*x*(1+11*x+11*x^2+x^3)/(1-x)^5)) \\ Altug Alkan, Mar 31 2016 CROSSREFS Cf. similar sequences of the form k*n^m, for k = 1...5, m = 1...10: A001477(k = 1, m = 1), A005843 (k = 2, m = 1), A008585 (k = 3, m = 1), A008586 (k = 4, m = 1), A008587 (k = 5, m = 1), A000290 (k = 1, m = 2), A001105 (k = 2, m = 2), A033428 (k = 3, m = 2), A016742 (k = 4, m = 2), A033429 (k = 5, m = 2), A000578 (k = 1, m = 3), A033431 (k = 2, m = 3), A117642 (k = 3, m = 3), A033430 (k = 4, m = 3), A244725 (k = 5, m = 3), A000583 (k = 1, m = 4), A244730 (k = 2, m = 4), A219056 (k = 3, m = 4), A141046 (k = 4, m = 4), this sequence(k = 5, m = 4), A000584 (k = 1, m = 5), A001014 (k = 1, m = 6), A106318 (k = 2, m = 6), A001015 (k = 1, m = 7), A001016 (k = 1, m = 8), A001017 (k = 1, m = 9), A008454 (k = 1, m = 10). Sequence in context: A062250 A131284 A105917 * A144344 A062364 A277302 Adjacent sequences:  A269789 A269790 A269791 * A269793 A269794 A269795 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Mar 31 2016 STATUS approved

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Last modified December 12 16:06 EST 2018. Contains 318077 sequences. (Running on oeis4.)