OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..254
FORMULA
a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^2 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).
EXAMPLE
The coefficients in the square of the series:
S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...
begin: [(1),(2,1),(2,2,0),(3,2,0,2),(2,2,1,2,0),(2,4,0,2,0,1),...];
the sums of the grouped coefficients yield the initial terms of this sequence.
MATHEMATICA
t[n_, k_] := Module[{s = Sum[x^(m*(m+1)/2), {m, 0, k+1}]+O[x]^((k+1)*(k+2)/2)}, Sum[Coefficient[s^n, x, m], {m, k*(k+1)/2, k*(k+1)/2+k}]]; Table[t[2, k], {k, 0, 68}] (* Jean-François Alcover, Nov 18 2013 *)
PROG
(PARI) {a(n)=local(S=sum(m=0, n+1, x^(m*(m+1)/2))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2, n*(n+1)/2+n, polcoeff(S^2, m))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2009
STATUS
approved