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A098613
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Expansion of q^(-5/24)eta(q^4)^2/(eta(q)eta(q^2)) in powers of q.
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2
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1, 1, 3, 4, 7, 10, 17, 23, 35, 48, 69, 93, 131, 173, 236, 310, 413, 536, 704, 903, 1170, 1489, 1904, 2403, 3044, 3811, 4784, 5951, 7409, 9157, 11325, 13912, 17095, 20891, 25519, 31029, 37708, 45632, 55184, 66495, 80050, 96064, 115173, 137680, 164425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Euler transform of period 4 sequence [1,2,1,0,...].
G.f. A(x) is limit of x^(n^2+n)P_{2n+1}(1/x)/2 where P_n(q) = Sum_{k=0..n} C(n,k;q) and C(n,k;q) is q-binomial coefficients.
This sequence convolved with A000009 gives A001936. [Gary W. Adamson, Mar 24 2011].
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FORMULA
| G.f.: (Sum_{k>0} x^(k^2-k))/(Product_{k>0} (1-x^k)).
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PROG
| (PARI) a(n)= if(n<0, 0, polcoeff( sum(k=0, (sqrtint(4*n+1)-1)\2, x^(k^2+k))/eta(x+x*O(x^n)), n))
(PARI) a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)^2/(eta(x+A)*eta(x^2+A)), n))
(PARI) a(n)= if(n<0, 0, polcoeff( sum(k=0, 2*n+1, prod(i=1, k, (1-x^(2*n+2-i))/(1-x^i)))/2, n^2))
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CROSSREFS
| Sequence in context: A147955 A134591 A058611 * A143607 A193826 A032715
Adjacent sequences: A098610 A098611 A098612 * A098614 A098615 A098616
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Sep 17 2004
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