A166942 One fifth of product plus sum of five consecutive nonnegative numbers.

2, 27, 148, 509, 1350, 3031, 6056, 11097, 19018, 30899, 48060, 72085, 104846, 148527, 205648, 279089, 372114, 488395, 632036, 807597, 1020118, 1275143, 1578744, 1937545, 2358746, 2850147, 3420172, 4077893, 4833054, 5696095

Offset

0,1

Comments

a(n) = ((n*...*(n+4))+(n+...+(n+4)))/5, n >= 0.

Binomial transform of 2, 25, 96, 144, 96, 24, 0, 0, 0, 0, ....

Partial sums of A062938 where initial term 1 is replaced by 2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = (n^5 + 10n^4 + 35n^3 + 50n^2 + 29n + 10)/5. - Charles R Greathouse IV, Nov 02 2009

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + 24 for n > 4; a(0)=2, a(1)=27, a(2)=148, a(3)=509, a(4)=1350. - Klaus Brockhaus, Nov 14 2009

G.f.: (2+15*x+16*x^2-14*x^3+6*x^4-x^5)/(1-x)^6. - Klaus Brockhaus, Nov 14 2009

Example

a(0) = (0*1*2*3*4 + 0 + 1 + 2 + 3 + 4)/5 = (0 + 10)/5 = 2.
a(1) = (1*2*3*4*5 + 1 + 2 + 3 + 4 + 5)/5 = (120 + 15)/5 = 27.

Mathematica

Table[((n+4)*(n+3)*(n+2)*(n+1)*n+(n+4)+(n+3)+(n+2)+(n+1)+n)/5, {n, 0, 100}]
(Total[#]+Times@@#)/5&/@Partition[Range[0, 100], 5, 1]  (* Harvey P. Dale, Mar 05 2011 *)

Prog

(Magma) [ (&*s + &+s)/5 where s is [n..n+4]: n in [0..29] ]; // Klaus Brockhaus, Nov 14 2009

Crossrefs

Cf. A001477 (nonnegative integers), A062938 (squares of the form n(n+1)(n+2)(n+3)+1), A028387 (n+(n+1)^2), A167875, A166941, A166943.

Sequence in context: A038625 A280089 A041801 * A119351 A098627 A263930

Adjacent sequences: A166939 A166940 A166941 * A166943 A166944 A166945

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 24 2009

Extensions

Edited and offset corrected by Klaus Brockhaus, Nov 14 2009

Status

approved