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A162432 Row 3 of table A162430. 7
1, 6, 13, 25, 39, 52, 81, 97, 129, 154, 187, 234, 250, 321, 337, 406, 468, 493, 579, 613, 699, 766, 811, 918, 979, 1056, 1141, 1212, 1357, 1408, 1485, 1639, 1698, 1810, 1908, 2050, 2152, 2250, 2398, 2523, 2629, 2770, 2934, 2986, 3219, 3280, 3522, 3598, 3739 (list; graph; refs; listen; history; text; internal format)
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)^3 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).

EXAMPLE

The coefficients in the cube of the series:

S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...

begin: [(1),(3,3),(4,6,3),(6,9,3,7),(9,6,9,9,6),(6,15,9,7,12,3),...];

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[3, k], {k, 0, 48}] (* 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^3, m))}

CROSSREFS

Cf. A162430, A162431, A162433, A162434, A162435, A162426 (variant).

Sequence in context: A058535 A131833 A101736 * A117072 A081395 A192762

Adjacent sequences:  A162429 A162430 A162431 * A162433 A162434 A162435

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 03 2009

STATUS

approved

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)