|
| |
|
|
A114921
|
|
Expansion of a q-series.
|
|
0
| |
|
|
1, 0, 1, 2, 4, 6, 11, 16, 27, 40, 63, 92, 141, 202, 299, 426, 614, 862, 1222, 1694, 2362, 3242, 4456, 6054, 8229, 11072, 14891, 19872, 26477, 35050, 46320, 60866, 79827, 104194, 135703, 176008, 227791, 293702, 377874, 484554, 620011, 790952, 1006924
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
FORMULA
| G.f.: 1+Sum_{k>0} (x^k/((1-x)(1-x^2)...(1-x^k)))^2 = (1+ Sum_{k>0} 2(-1)^k x^((k^2+k)/2) )/(Product_{k>0}(1-x^k))^2.
|
|
|
PROG
| (PARI) {a(n)=if(n<0, 0, polcoeff( sum(k=0, n\2, x^(2*k)/prod(i=1, k, 1-x^i, 1+x*O(x^n))^2), n))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( sum(k=1, sqrtint(8*n+1)\2, 2*(-1)^k*x^((k^2+k)/2), 1+A)/eta(x+A)^2, n))}
|
|
|
CROSSREFS
| Sequence in context: A062766 A115269 A103692 * A103442 A056342 A094719
Adjacent sequences: A114918 A114919 A114920 * A114922 A114923 A114924
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Michael Somos, Jan 07 2006
|
| |
|
|
