A256453 Expansion of cusp form for Gamma1(11) of weight 3 in powers of q with expansion being q^5 + ...

1, -5, 8, -2, -5, 4, -11, 19, -2, -6, -9, -7, 26, -2, -7, -4, -6, 11, -5, -7, 12, 12, 4, -32, -20, 28, 23, 1, 0, -52, 24, 7, 5, 12, -10, -8, -11, 12, -1, 33, -28, -2, -32, 22, 12, 9, 26, -26, -40, -19, 33, 44, -8, 18, -33, -32, 34, -44, 8, 58, 16, -66, 7, -13

Offset

5,2

Links

G. C. Greubel, Table of n, a(n) for n = 5..1000

Formula

Euler transform of period 11 sequence [-5, -2, -2, -1, 1, 1, -1, -2, -2, -5, -6, ...].

Example

G.f. = q^5 - 5*q^6 + 8*q^7 - 2*q^8 - 5*q^9 + 4*q^10 - 11*q^11 + 19*q^12 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q^5 Product[(1 - q^k)^{5, 2, 2, 1, -1, -1, 1, 2, 2, 5, 6}[[Mod[k, 11, 1]]], {k, 1, n - 5}], {q, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<5, 0, n -= 5; A = 1 + x * O(x^n); polcoeff( prod(k=1, n, (1 - x^k)^[6, 5, 2, 2, 1, -1, -1, 1, 2, 2, 5][k%11 + 1], A), n))};
(Magma) Basis( CuspForms( Gamma1(11), 3), 69) [5];

Crossrefs

Sequence in context: A180155 A110989 A099736 * A276627 A119420 A134469

Adjacent sequences: A256450 A256451 A256452 * A256454 A256455 A256456

Keyword

sign

Author

Michael Somos, Mar 29 2015

Status

approved