A143060 a(n) = (n^5 + 145*n^4 + 905*n^3 + 155*n^2 + 594*n + 120)/120.

1, 16, 96, 331, 842, 1782, 3337, 5727, 9207, 14068, 20638, 29283, 40408, 54458, 71919, 93319, 119229, 150264, 187084, 230395, 280950, 339550, 407045, 484335, 572371, 672156, 784746, 911251, 1052836, 1210722, 1386187, 1580567, 1795257, 2031712, 2291448, 2576043, 2887138

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

Binomial transform of [1, 15, 65, 90, 31, 1, 0, 0, 0, ...] where (1, 15, 65 90, 31, 1) = row 6 of triangle A008278.

a(n) = 1 + 15*n + 65*binomial(n,2) + 90*binomial(n,3) + 31*binomial(n,4) + binomial(n,5).

G.f.: (1+10*x+15*x^2-25*x^3-9*x^4+9*x^5)/(1-x)^6. - Colin Barker, Feb 01 2012

Example

a(3) = 96 = (1, 2, 1) dot (1, 15, 65) = (1 + 30 + 65).

Crossrefs

Cf. A143058, A143059, A008278.

Sequence in context: A322639 A277044 A192037 * A006637 A241937 A014344

Adjacent sequences: A143057 A143058 A143059 * A143061 A143062 A143063

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 20 2008

Extensions

New name, offset corrected and a(31) onwards from Andrew Howroyd, Sep 24 2025

Status

approved