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A202943 G.f.: [ Sum_{n>=0} (n+1)*(n+2)/2 * 2^(n*(n-1)) * x^n ]^(1/3). 3
1, 1, 7, 199, 20026, 7296946, 10006653574, 52756427071846, 1080758244198360481, 86574556540356639703921, 27234507698931717202501389871, 33749875110161915818408975272861391, 165150307912136693948216143106251788630208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare g.f. to: [Sum_{n>=0} (n+1)*(n+2)/2 * x^n ]^(1/3) = 1/(1-x).

Conjecture: the characteristic function of a(n) (mod 2) equals (1+x)*(1+x^2)*(1+x^8) * Sum_{n>0} x^(32*A000695(n)), where A000695 is the sums of distinct powers of 4.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..50

FORMULA

a(n) == 1 (mod 3).

EXAMPLE

G.f.: A(x) = 1 + x + 7*x^2 + 199*x^3 + 20026*x^4 + 7296946*x^5 +...

where

A(x)^3 = 1 + 3*x + 6*2^2*x^2 + 10*2^6*x^3 + 15*2^12*x^4 + 21*2^20*x^5 +...

more explicitly,

A(x)^3 = 1 + 3*x + 24*x^2 + 640*x^3 + 61440*x^4 + 22020096*x^5 +...+ A202944(n)*x^n +...

The residues modulo 2 of this sequence begin:

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,...];

which forms the characteristic function:

(1+x)*(1+x^2)*(1+x^8)*(1 + x^32 + x^128 + x^160 + x^512 + x^544 + x^640 + x^672 +...+ x^(32*A000695(n)) +...).

PROG

(PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)/2*2^(m*(m-1))*x^m+x*O(x^n))^(1/3), n)}

CROSSREFS

Cf. A202944, A202942, A202980.

Sequence in context: A206473 A300616 A178319 * A057204 A124988 A220934

Adjacent sequences:  A202940 A202941 A202942 * A202944 A202945 A202946

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 26 2011

STATUS

approved

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Last modified August 4 03:18 EDT 2021. Contains 346442 sequences. (Running on oeis4.)