A151626 Number of permutations of 2 indistinguishable copies of 1..n with exactly 4 adjacent element pairs in decreasing order.

0, 0, 1, 603, 47290, 1822014, 49258935, 1086859301, 21147576440, 379269758400, 6441229796061, 105398150289775, 1680774708581766, 26324724399068626, 407112461900381715, 6239897666881158537, 95036195852840662820, 1440959515956284422196, 21778829725476446172249

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (70, -2163, 39122, -462914, 3792972, -22214806, 94629124, -295393077, 675442494, -1122134391, 1331169066, -1093400856, 588623760, -186332400, 26244000).

Formula

a(n) = 15^n - (2*n + 1)*10^n + binomial(2*n+1, 2)*6^n - binomial(2*n+1, 3)*3^n + binomial(2*n+1, 4). - Andrew Howroyd, May 07 2020

From G. C. Greubel, Sep 07 2022: (Start)

G.f.: x^3*(1 + 533*x + 7243*x^2 - 223119*x^3 + 878573*x^4 + 5014923*x^5 - 40074183*x^6 + 75062403*x^7 + 19732086*x^8 - 185394420*x^9 + 117543960*x^10 + 43740000*x^11)/((1-x)^5*(1-3*x)^4*(1-6*x)^3*(1-10*x)^2*(1-15*x)).

E.g.f.: exp(15*x) - (1+20*x)*exp(10*x) + 18*x*(1+4*x)*exp(6*x) - 3*x*(1 + 12*x + 12*x^2)*exp(3*x) + (x^2/6)*(15 + 20*x + 4*x^2)*exp(x). (End)

Mathematica

With[{B=Binomial}, Table[Sum[(-1)^(j+1)*B[2n+1, 5-j]*B[j+1, 2]^n, {j, 5}], {n, 30}]] (* G. C. Greubel, Sep 07 2022 *)

Prog

(PARI) a(n) = {15^n - (2*n + 1)*10^n + binomial(2*n+1, 2)*6^n - binomial(2*n+1, 3)*3^n + binomial(2*n+1, 4) } \\ Andrew Howroyd, May 07 2020
(Magma)
A151626:= func< n | (&+[(-1)^(j+1)*Binomial(2*n+1, 5-j)*Binomial(j+1, 2)^n: j in [1..5]]) >;
[A151626(n): n in [1..30]]; // G. C. Greubel, Sep 07 2022
(SageMath)
@CachedFunction
def A151626(n): return sum((-1)^(j+1)*binomial(2*n+1, 5-j)*binomial(j+1, 2)^n for j in (1..5))
[A151626(n) for n in (1..30)] # G. C. Greubel, Sep 07 2022

Crossrefs

Column k=4 of A154283.

Sequence in context: A177685 A250907 A209550 * A031792 A020383 A234109

Adjacent sequences: A151623 A151624 A151625 * A151627 A151628 A151629

Keyword

nonn

Author

R. H. Hardin, May 29 2009

Extensions

Terms a(12) and beyond from Andrew Howroyd, May 07 2020

Status

approved