login
A162433
Row 4 of table A162430.
7
1, 10, 33, 76, 157, 264, 425, 626, 897, 1230, 1629, 2174, 2653, 3448, 4119, 4978, 6197, 7114, 8457, 9870, 11477, 13070, 15001, 17104, 19181, 21732, 24327, 26926, 30247, 33232, 36695, 40674, 44065, 48554, 52827, 57664, 62361, 67704, 73347, 78728
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^4 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).
EXAMPLE
The coefficients in the 4th power of the series:
S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...
begin: [(1),(4,6),(8,13,12),(14,24,18,20),(32,24,31,40,30),...];
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)}, k*(k+1)/2+k}]]; Table[t[4, k], {k, 0, 39}] (* 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^4, m))}
CROSSREFS
Sequence in context: A081437 A085490 A367014 * A003012 A020478 A094170
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2009
STATUS
approved