A025278 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.

1, -1, 1, 1, 0, -1, 0, 3, 4, 0, -2, 11, 34, 36, 14, 55, 250, 484, 526, 672, 2024, 5106, 8388, 11415, 21806, 53222, 107954, 176392, 295988, 615242, 1316100, 2462955, 4271142, 8015318, 16478474, 32815776, 60660164, 111589258, 218042964, 436588372

Offset

1,8

Links

Table of n, a(n) for n=1..40.

Formula

Conjecture: n*(n^4+n^3+n^2+n+1)*a(n) +(n^5+n^4+n^3+n^2+n+5)*a(n-1) +(n^5+n^4+n^3+n^2+n-52)*a(n-2) +12*(-2*n^5+5*n^4+3*n^3+2*n^2+3*n+24)*a(n-3) +2*(26*n^5-103*n^4-58*n^3-37*n^2-64*n-371)*a(n-4) +2*(-58*n^5+329*n^4+209*n^3+143*n^2+185*n+713)*a(n-5) +8*(n-8)*(13*n^4+9*n^3+7*n^2+9*n+19)*a(n-6)=0. - R. J. Mathar, Jan 25 2015

G.f.: 1/2 - sqrt(8*x^4-12*x^3+8*x^2-4*x+1)/2. - Vaclav Kotesovec, Jan 25 2015

Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) - 8*(n-3)*a(n-2) + 6*(2*n-9)*a(n-3) - 8*(n-6)*a(n-4). - Vaclav Kotesovec, Jan 25 2015

Mathematica

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = -1; aa[[3]] = 1; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]], {k, 1, n-1}], {n, 5, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)

Crossrefs

Sequence in context: A228550 A354520 A189916 * A200514 A063405 A360533

Adjacent sequences: A025275 A025276 A025277 * A025279 A025280 A025281

Keyword

sign

Author

Clark Kimberling

Status

approved