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

Author

R. H. Hardin, May 29 2009

Keywords

• nonn

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).

Crossrefs

Column k=5 of A174266.

Programs

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 *)

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

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

Extensions

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