A162433 Row 4 of table A162430.

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

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-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

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

Sequence in context: A081437 A085490 A367014 * A003012 A020478 A094170

Adjacent sequences: A162430 A162431 A162432 * A162434 A162435 A162436

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2009

Status

approved