A151635 Number of permutations of 3 indistinguishable copies of 1..n with exactly 5 adjacent element pairs in decreasing order.

0, 0, 54, 128124, 40241088, 5904797049, 592030140912, 47871255785661, 3399596932632516, 222507204130403730, 13816730633213564154, 828855022115369147634, 48598186867956968680368, 2806334420165022553155783, 160409202733612103932779012, 9106532681255976991378628043

Offset

1,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (252, -28116, 1847460, -80186430, 2443408020, -54222394300, 897042522780, -11233051883145, 107495660310160, -790365294823704, 4473663278780448, -19473246213545104, 64926170063690880, -164639495047219200, 314180023114240000, -444424489989120000, 455945899622400000, -328038555648000000, 156378808320000000, -44255232000000000, 5619712000000000).

Formula

a(n) = Sum_{j=0..7} (-1)^(j+1)*binomial(3*n+1, 7-j)*(binomial(j+1, 3))^n. - G. C. Greubel, Mar 26 2022

Mathematica

T[n_, k_]:= T[n, k]= Sum[(-1)^(k-j)*Binomial[3*n+1, k-j+2]*(Binomial[j+1, 3])^n, {j, 0, k+2}];
Table[T[n, 5], {n, 30}] (* G. C. Greubel, Mar 26 2022 *)

Prog

(Sage)
@CachedFunction
def T(n, k): return sum( (-1)^(k-j)*binomial(3*n+1, k-j+2)*(binomial(j+1, 3))^n for j in (0..k+2) )
[T(n, 5) for n in (1..30)] # G. C. Greubel, Mar 26 2022

Crossrefs

Column k=5 of A174266.

Sequence in context: A071800 A093254 A347061 * A363458 A218430 A159732

Adjacent sequences: A151632 A151633 A151634 * A151636 A151637 A151638

Keyword

nonn

Author

R. H. Hardin, May 29 2009

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 06 2020

Status

approved