A145127 a(n) = 1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120.

1, 3, 9, 25, 61, 132, 259, 470, 801, 1297, 2013, 3015, 4381, 6202, 8583, 11644, 15521, 20367, 26353, 33669, 42525, 53152, 65803, 80754, 98305, 118781, 142533, 169939, 201405, 237366, 278287, 324664, 377025, 435931, 501977, 575793, 658045, 749436

Offset

0,2

Comments

(1 + 3x + 9x^2 + ...) = (1 + 3x + 6x^2 + 10x^3 + ...) * (1 + 3x^2 + 6x^3 + 10x^4 + ...). - Gary W. Adamson, Jul 27 2010

Links

Vincenzo Librandi, 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

G.f.: (x^4 - 4*x^3 + 6*x^2 - 3*x + 1) / (1-x)^6.

E.g.f.: exp(x)*(120 + 240*x + 240*x^2 + 120*x^3 + 20*x^4 + x^5)/120. - Stefano Spezia, Sep 09 2025

Maple

a:= n-> 1+ (144+ (50+ (35+ (10+ n) *n) *n) *n) *n/120:
seq(a(n), n=0..40);

Prog

(Magma) [1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120: n in [0..40]]; // Vincenzo Librandi, May 19 2011

Crossrefs

6th row of A145153. See row 6 of A145140/A145141 for rational coefficients and A145142 for 120 * coefficients of polynomial.

Sequence in context: A101357 A004255 A065971 * A096260 A385689 A375135

Adjacent sequences: A145124 A145125 A145126 * A145128 A145129 A145130

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 03 2008

Status

approved