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 A075915 Seventh column of triangle A075500. 3
 1, 140, 11550, 735000, 39991875, 1960612500, 89303500000, 3853850000000, 159664583203125, 6409926960937500, 251055710800781250, 9641722822265625000, 364483553427490234375, 13602971247133789062500, 502386213470141601562500, 18394848021467285156250000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The e.g.f. given below is Sum_{m=0..6}(A075513(7,m)exp(5*(m+1)*x))/6!. LINKS Colin Barker, Table of n, a(n) for n = 0..646 Index entries for linear recurrences with constant coefficients, signature (140,-8050,245000,-4230625,41037500,-204187500,393750000). FORMULA a(n) = A075500(n+7, 7) = (5^n)S2(n+7, 7) with S2(n, m) = A008277(n, m) (Stirling2). a(n) = Sum_{m=0..6}(A075513(7, m)*(5*(m+1))^n)/6!. G.f.: 1/Product_{k=1..7}(1-5k*x). E.g.f.: (d^7/dx^7)((((exp(5x)-1)/5)^7)/7!) = (exp(5*x) - 384*exp(10*x) + 10935*exp(15*x) - 81920*exp(20*x) + 234375*exp(25*x) - 279936*exp(30*x) + 117649*exp(35*x))/6!. G.f.: 1 / ((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)). - Colin Barker, Dec 12 2015 MATHEMATICA Table[5^(n-1) * (1 - 3*2^(7 + n) - 5*2^(14 + 2*n) + 5*3^(7 + n) + 3*5^(7 + n) - 6^(7 + n) + 7^(6 + n))/144, {n, 0, 20}] (* Vaclav Kotesovec, Dec 12 2015 *) PROG (PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)) + O(x^30)) \\ Colin Barker, Dec 12 2015 CROSSREFS Cf. A000351, A016164, A075911, A075912, A075913, A075914. Sequence in context: A282613 A202786 A035820 * A159362 A188255 A159366 Adjacent sequences: A075912 A075913 A075914 * A075916 A075917 A075918 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 02 2002 STATUS approved

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Last modified April 22 09:42 EDT 2024. Contains 371894 sequences. (Running on oeis4.)