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 A289694 The number of partitions of [n] with exactly 4 blocks without peaks. 2
 0, 0, 0, 1, 4, 16, 64, 236, 818, 2736, 8934, 28622, 90324, 281792, 871556, 2677750, 8184383, 24913238, 75593383, 228793147, 691094857, 2084237036, 6277871658, 18890568921, 56798001639, 170665733660, 512554832309, 1538718547049 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..28. T. Mansour and M. Shattuck, Counting Peaks and Valleys in a Partition of a Set, J. Int. Seq. 13 (2010), 10.6.8, Table 1. Index entries for linear recurrences with constant coefficients, signature (10,-45,130,-280,471,-643,734,-701,575,-400,237,-121,49,-18,4,-1). FORMULA G.f. x^4*(x^2-x+1)*(x^4-x^3+3*x^2-2*x+1)*(x^6-x^5+5*x^4-4*x^3+6*x^2-3*x+1) / ( (x-1)*(x^5-x^4+4*x^3-3*x^2+3*x-1)*(x^7-x^6+6*x^5-5*x^4+10*x^3-6*x^2+4*x-1)*(x^3-x^2+2*x-1) ). - R. J. Mathar, Mar 11 2021 a(n)= 10*a(n-1) -45*a(n-2) +130*a(n-3) -280*a(n-4) +471*a(n-5) -643*a(n-6) +734*a(n-7) -701*a(n-8) +575*a(n-9) -400*a(n-10) +237*a(n-11) -121*a(n-12) +49*a(n-13) -18*a(n-14) +4*a(n-15) -a(n-16). - R. J. Mathar, Mar 11 2021 MAPLE with(orthopoly) : nmax := 15: tpr := 1+x^2/2 : k := 4: g := x^k ; for j from 1 to k do if j> 1 then g := g*( U(j-1, tpr)-(1+x)*U(j-2, tpr)) / ((1-x)*U(j-1, tpr)-U(j-2, tpr)) ; else # note that U(-1, .)=0, U(0, .)=1 g := g* U(j-1, tpr) / ((1-x)*U(j-1, tpr)) ; end if; end do: simplify(%) ; taylor(g, x=0, nmax+1) ; gfun[seriestolist](%) ; # R. J. Mathar, Mar 11 2021 CROSSREFS Cf. A289692 (2 blocks), A289693 (3 blocks). Sequence in context: A248088 A294037 A228735 * A232425 A180239 A006811 Adjacent sequences: A289691 A289692 A289693 * A289695 A289696 A289697 KEYWORD nonn,easy AUTHOR R. J. Mathar, Jul 09 2017 STATUS approved

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Last modified November 28 04:05 EST 2023. Contains 367394 sequences. (Running on oeis4.)