A393841 a(n) is the number of n-digit terms in A393832.

1, 0, 108, 660, 2622, 8346, 22914, 56358, 127125, 267247, 529777, 999163, 1805353, 3142555, 5293717, 8661943, 13810222, 21511018, 32807450, 49087982, 72176744, 104441816, 148924028, 209489060, 291005867, 399554705, 542668295, 729609933, 971692635, 1282643697, 1679019351

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Index entries for sequences related to compositions.

Formula

a(n) = Sum_{m=2..9} Sum_{k=2..m} binomial(m-1,k-1)*(n*binomial(n-1,n-k-1) - (n - 1)*binomial(n-2,n-k-2)) for n > 1.

a(n) = (6168960 - 6536880*n + 37332*n^2 + 117548*n^3 + 124551*n^4 + 65730*n^5 + 19278*n^6 + 3192*n^7 + 279*n^8 + 10*n^9)/362880 for n > 1.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 11.

Limit_{n->oo} a(n+1)/a(n) = 1.

G.f.: x*(1 - 10*x + 153*x^2 - 540*x^3 + 1092*x^4 - 1386*x^5 + 1134*x^6 - 588*x^7 + 180*x^8 - 27*x^9 + x^10)/(1 - x)^10.

E.g.f.: exp(x)*(17 - 17*x + 17*x^2/2 + 91*x^3/6 + 245*x^4/24 + 77*x^5/24 + 371*x^6/720 + 31*x^7/720 + 71*x^8/40320 + x^9/36288) - 17 + x.

Mathematica

a[1]=1; a[n_]:=(6168960 - 6536880*n + 37332*n^2 + 117548*n^3 + 124551*n^4 + 65730*n^5 + 19278*n^6 + 3192*n^7 + 279*n^8 + 10*n^9)/362880; Array[a, 31]

Crossrefs

Cf. A097805, A393832.

Sequence in context: A204276 A202194 A386433 * A333757 A203373 A292343

Adjacent sequences: A393838 A393839 A393840 * A393843 A393844 A393845

Keyword

nonn,base,easy

Author

Stefano Spezia, Mar 01 2026

Status

approved