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A027622 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4 + (n+4)^5. 2
1114, 3413, 8476, 18247, 35414, 63529, 107128, 171851, 264562, 393469, 568244, 800143, 1102126, 1488977, 1977424, 2586259, 3336458, 4251301, 5356492, 6680279, 8253574, 10110073, 12286376, 14822107, 17760034, 21146189, 25029988, 29464351, 34505822, 40214689 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2

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

FORMULA

From Colin Barker, Dec 05 2016: (Start)

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

G.f.: (1114-3271*x+4708*x^2-3694*x^3+1522*x^4-259*x^5) / (1-x)^6.

(End)

MATHEMATICA

Table[n + (n + 1)^2 + (n + 2)^3 + (n + 3)^4 + (n + 4)^5, {n, 0, 29}] (* Alonso del Arte, Nov 22 2016 *)

Table[ReleaseHold@ Total@ MapIndexed[#1^First@ #2 &, Rest@ FactorList[ Pochhammer[Hold@ n, 5]][[All, 1]]], {n, 0, 29}] (* or *)

CoefficientList[Series[(1114 - 3271 x + 4708 x^2 - 3694 x^3 + 1522 x^4 - 259 x^5)/(1 - x)^6, {x, 0, 29}], x] (* Michael De Vlieger, Dec 05 2016 *)

PROG

(MAGMA)[n+(n+1)^2+(n+2)^3+(n+3)^4+(n+4)^5: n in [0..30]]; // Vincenzo Librandi, Dec 28 2010

(PARI) Vec((1114-3271*x+4708*x^2-3694*x^3+1522*x^4-259*x^5) / (1-x)^6 + O(x^30)) \\ Colin Barker, Dec 05 2016

CROSSREFS

Cf. A027621.

Sequence in context: A199982 A151951 A190017 * A259295 A260103 A258691

Adjacent sequences:  A027619 A027620 A027621 * A027623 A027624 A027625

KEYWORD

nonn,easy,changed

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 10 15:32 EST 2016. Contains 279003 sequences.