A134631 - OEIS

A134631

a(n) = 5*n^5 - 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.

0, 4, 144, 1152, 4960, 15300, 38304, 83104, 162432, 293220, 497200, 801504, 1239264, 1850212, 2681280, 3787200, 5231104, 7085124, 9430992, 12360640, 15976800, 20393604, 25737184, 32146272, 39772800, 48782500, 59355504, 71686944, 85987552, 102484260, 121420800, 143058304, 167675904, 195571332, 227061520

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OFFSET

0,2

LINKS

Harvey P. Dale, 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

a(n) = 5*n^5 - 3*n^3 + 2*n^2.

G.f.: 4x*(1+30x+87x^2+32x^3)/(1-x)^6. - R. J. Mathar, Nov 14 2007

EXAMPLE

a(4)=4960 because 4^5=1024, 5*1024=5120, 4^3=64, 3*64=192, 4^2=16, 2*16=32 and we can write 5120 - 192 + 32 = 4960.

MATHEMATICA

Table[5n^5-3n^3+2n^2, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 4, 144, 1152, 4960, 15300}, 40] (* Harvey P. Dale, Jan 20 2023 *)

PROG

(Magma)[5*n^5-3*n^3+2*n^2: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010

CROSSREFS

Cf. A000290, A000578, A000584, A045991, A100019, A133071.

Sequence in context: A053897 A017294 A273698 * A036511 A263386 A186720

Adjacent sequences: A134628 A134629 A134630 * A134632 A134633 A134634

KEYWORD

nonn

AUTHOR

Omar E. Pol, Nov 04 2007

EXTENSIONS

More terms from Vincenzo Librandi, Dec 14 2010

STATUS

approved