A008271 Number of performances of n fragments in Stockhausen problem.

0, 2, 114, 5844, 380900, 32817990, 3679720422, 524366318504, 92857556215944, 20037507147592650, 5180981746936701530, 1582222025035216228092, 563668692910591272692844, 231745357332413891454727694

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..230

R. C. Read, Combinatorial problems in theory of music, Discrete Math. 167 (1997), 543-551.

Ronald C. Read, Lily Yen, A note on the Stockhausen problem, J. Comb. Theory, Ser. A 76, No. 1 (1996), 1-10.

Formula

Recurrence: (n-2)*(3*n-7)*a(n) = (n-1)*n*(6*n^2 - 17*n + 16)*a(n-1) - (n-1)*n*(12*n^2 - 37*n + 29)*a(n-2) + 2*(n-2)*(n-1)*n*(3*n-4)*a(n-3). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n+3/2) / exp(2*n). - Vaclav Kotesovec, Feb 18 2015

Mathematica

Table[n*Sum[Binomial[n-1, i]*(2*i)!*i*(2*i-1)/2^i, {i, 0, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Feb 18 2015 after R. C. Read *)

Prog

(PARI) for(n=1, 25, print1(n*sum(k=0, n-1, binomial(n-1, k)*(2*k)!*k*(2*k-1)/2^k), ", ")) \\ G. C. Greubel, Apr 11 2017

Crossrefs

Sequence in context: A230471 A140986 A157068 * A362575 A209184 A356724

Adjacent sequences: A008268 A008269 A008270 * A008272 A008273 A008274

Keyword

nonn

Author

Lily Yen

Status

approved