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A162431 Row 2 of table A162430. 7
1, 3, 4, 7, 7, 9, 12, 11, 15, 14, 19, 19, 19, 22, 23, 27, 26, 27, 31, 30, 33, 35, 35, 40, 39, 39, 40, 47, 47, 47, 46, 51, 53, 52, 55, 55, 61, 60, 57, 67, 62, 69, 65, 64, 77, 71, 77, 72, 75, 83, 76, 81, 85, 85, 88, 85, 91, 92, 91, 95, 92, 103, 97, 99, 102, 105, 107, 104, 111 (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)^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-Fran├žois 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

Cf. A162430, A162432, A162433, A162434, A162435, A162425 (variant).

Sequence in context: A023849 A197034 A180020 * A024605 A215630 A168563

Adjacent sequences:  A162428 A162429 A162430 * A162432 A162433 A162434

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 03 2009

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)