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A061224 a(n) = n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5. 1
260, 1114, 3412, 8474, 18244, 35410, 63524, 107122, 171844, 264554, 393460, 568234, 800132, 1102114, 1488964, 1977410, 2586244, 3336442, 4251284, 5356474, 6680260, 8253554, 10110052, 12286354, 14822084, 17760010, 21146164, 25029962 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

FORMULA

G.f.: 2*(130 - 223*x + 314*x^2 - 244*x^3 + 100*x^4 - 17*x^5)/(1-x)^6. - Bruno Berselli, Aug 05 2011

E.g.f.: exp(x)*(260 + 854*x + 722*x^2 + 220*x^3 + 26*x^4 + x^5). - Stefano Spezia, Nov 02 2018

EXAMPLE

a(1) = 1 + 2^3 + 3^4 + 4^5 = 1 + 8 + 81 + 1024 = 1114.

MAPLE

seq(n^2+(n+1)^3+(n+2)^4+(n+3)^5, n=0..30); # Muniru A Asiru, Nov 02 2018

MATHEMATICA

Table[n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5, {n, 0, 30}] (* G. C. Greubel, Nov 02 2018 *)

CoefficientList[Series[E^x (260 + 854 x + 722 x^2 + 220 x^3 + 26 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)

PROG

(MAGMA) [n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011

(PARI) vector(30, n, n--; n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5) \\ G. C. Greubel, Nov 02 2018

(GAP) List([0..30], n->n^2+(n+1)^3+(n+2)^4+(n+3)^5); # Muniru A Asiru, Nov 02 2018

CROSSREFS

Cf. A027621.

Sequence in context: A202585 A037219 A290040 * A108109 A235905 A287923

Adjacent sequences:  A061221 A061222 A061223 * A061225 A061226 A061227

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, May 31 2001

EXTENSIONS

Offset changed from 1 to 0 by Vincenzo Librandi, Aug 05 2011

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)