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A047807 Theta series of Niemeier lattice of type A_5^4*D_4. 1
1, 144, 193104, 16809408, 397822032, 4630076640, 34416785088, 187487524224, 814891939920, 2975535123408, 9486534607200, 27053022904128, 70486183583424, 169931012132448, 384163644219264, 820166796086400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

This series is the q-expansion of 2/3 E_4(z)^3 + 1/3 E_6(z)^2. Cf. A004009, A013973. - Daniel D. Briggs, Nov 25 2011

MATHEMATICA

terms = 16; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 2/3 E4[q]^3 + 1/3 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-Fran├žois Alcover, Jul 06 2017 *)

CROSSREFS

Equal to the theta series of D_4^6, A008700.

Sequence in context: A159724 A221124 A008700 * A023112 A159424 A013751

Adjacent sequences:  A047804 A047805 A047806 * A047808 A047809 A047810

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 05 2000

STATUS

approved

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Last modified August 18 12:24 EDT 2017. Contains 290720 sequences.