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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 (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)^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-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^4, m))}

CROSSREFS

Cf. A162430, A162431, A162432, A162434, A162435, A162427 (variant).

Sequence in context: A299285 A081437 A085490 * A003012 A020478 A094170

Adjacent sequences:  A162430 A162431 A162432 * A162434 A162435 A162436

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 03 2009

STATUS

approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)