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A096962 Sum_{0<d|n, n/d odd} d^9. 7
1, 512, 19684, 262144, 1953126, 10078208, 40353608, 134217728, 387440173, 1000000512, 2357947692, 5160042496, 10604499374, 20661047296, 38445332184, 68719476736, 118587876498, 198369368576, 322687697780, 512000262144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares, arXiv:math/0407061 [math.NT], 2004.

FORMULA

G.f.: Sum_{k>0} k^9 * x^k / (1 - x^(2*k)).

EXAMPLE

G.f. = q + 512*q^2 + 19684*q^3 + 262144*q^4 + 1953126*q^5 + 10078208*q^6 + ...

MATHEMATICA

a[ n_] := If[ n < 1, 0, Sum[ d^9 Boole[ OddQ[ n/d]], {d, Divisors[ n]}]]; (* Michael Somos, Jun 04 2013 *)

a[ n_] := SeriesCoefficient[ With[{u1 = QPochhammer[ q]^8, u2 = QPochhammer[ q^2]^4, u4 = QPochhammer[ q^4]^8}, q u2 (u1 + 32 q u4) (u1^2 + 496 q u4 u1 + 7936 q^2 u4^2 ) / u1], {q, 0, n}]; (* Michael Somos, Jun 04 2013 *)

PROG

(PARI) {a(n) = if( n<1, 0, sumdiv( n, d, (n/d%2) * d^9))}; /* Michael Somos, Jun 04 2013 */

(PARI) {a(n) = local(A, A1, A2, A4); if( n<1, 0, n--; A = x * O(x^n); A1 = eta(x + A)^8; A2 = eta(x^2 + A)^4; A4 = eta(x^4 + A)^8; polcoeff( A2 * (A1 + 32*x * A4) * (A1^2 + 496*x * A1*A4 + 7936*x^2 * A4^2) / A1, n))}; /* Michael Somos, Jun 04 2013 */

(Sage) ModularForms( Gamma0(2), 10, prec=33).2; # Michael Somos, Jun 04 2013

(MAGMA) A := Basis( ModularForms( Gamma0(2), 10), 21); A[2] + 512*A[3]; /* Michael Somos, Aug 25 2014 */

CROSSREFS

Cf. A007331, A096960, A096961, A096963.

Sequence in context: A050756 A179665 A056586 * A231308 A254735 A254914

Adjacent sequences:  A096959 A096960 A096961 * A096963 A096964 A096965

KEYWORD

nonn,mult

AUTHOR

Ralf Stephan, Jul 18 2004

STATUS

approved

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Last modified June 29 14:46 EDT 2022. Contains 354913 sequences. (Running on oeis4.)