A168305 The fourth left hand column of triangle A167580.

-15, -48, 2024, 31616, 274480, 1784320, 9645312, 45735936, 196441344, 780595200, 2912532480, 10315202560, 34963222528, 114140905472, 360716042240, 1108051230720, 3319564664832, 9726122262528, 27935264735232, 78810426900480, 218761889054720, 598349308755968

Offset: 4

Author

Johannes W. Meijer, Nov 23 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (16, -112, 448, -1120, 1792, -1792, 1024, -256).

Crossrefs

Equals the fourth left hand column of triangle A167580.

Other left hand columns are A014480, A167581, A167582 and A168306.

Programs

Magma

[2^n*(54*n^7-763*n^6+4158*n^5-11305*n^4+16401*n^3- 12502*n^2+4587*n-630)/10080: n in [4..40]]; // Vincenzo Librandi, Jul 18 2016

Mathematica

LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {-15, -48, 2024, 31616, 274480, 1784320, 9645312, 45735936}, 997] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = 2^n*(54*n^7 - 763*n^6 + 4158*n^5 - 11305*n^4 + 16401*n^3 - 12502*n^2 + 4587*n - 630)/10080.

G.f.: (16*z^4 + 576*z^3 + 1112*z^2 + 192*z - 15)/(2*z-1)^8.

a(n) = 16*a(n-1) - 112*a(n-2) + 448*a(n-3) - 1120*a(n-4) + 1792*a(n-5) - 1792*a(n-6) + 1024*a(n-7) - 256*a(n-8).

a(n) - 15*a(n-1) + 98*a(n-2) - 364*a(n-3) + 840*a(n-4) - 1232*a(n-5) + 1120*a(n-6) - 576*a(n-7) + 128*a(n-8) = 27*2^(n-1).