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 A274272 Number of partitions of 5^n into at most four parts. 2
 1, 6, 185, 15246, 1736385, 212946246, 26516391385, 3312004971246, 413937039016385, 51740540399346246, 6467527813385891385, 808439983261977471246, 101054973072475964016385, 12631871013177766274346246, 1578983861125177809948391385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..450 FORMULA Coefficient of x^(5^n) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)). Conjectures (Start) a(n) = (57+8*(-1)^n+63*5^n+3*5^(1+2*n)+125^n)/144. a(n) = 155*a(n-1)-3874*a(n-2)+15470*a(n-3)+3875*a(n-4)-15625*a(n-5) for n>4. G.f.: (1-149*x+3129*x^2-5655*x^3-6750*x^4) / ((1-x)*(1+x)*(1-5*x)*(1-25*x)*(1-125*x)). (End) PROG (PARI) \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)). b(n) = round(real(68+36*(-1)^n+18*((-I)^n+I^n)+(16*exp(-2/3*I*n*Pi)*(1+I*sqrt(3)+2*exp((4*I*n*Pi)/3)))/(1+(-1)^(1/3))+59*(1+n)+9*(-1)^n*(1+n)+18*(1+n)*(2+n)+2*(1+n)*(2+n)*(3+n))/288) vector(20, n, n--; b(5^n)) CROSSREFS A subsequence of A001400. Cf. A274100 (2^n), A274271 (3^n). Sequence in context: A012208 A012181 A012224 * A175237 A222335 A037298 Adjacent sequences:  A274269 A274270 A274271 * A274273 A274274 A274275 KEYWORD nonn AUTHOR Colin Barker, Jun 17 2016 STATUS approved

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Last modified May 16 08:07 EDT 2022. Contains 353695 sequences. (Running on oeis4.)