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A121372 Triangle, read by rows of length A003056(n) for n>=1, defined by the recurrence: T(n,k) = T(n-k,k-1) - T(n-k,k) for n>k>1, with T(n,1)=(-1)^(n-1) for n>=1. 0
1, -1, 1, 1, -1, -1, 1, 0, -1, 0, 1, 1, 1, -1, -1, -1, 0, 1, 0, -1, -1, 0, 2, 1, 1, 1, -1, -1, -1, -1, 1, 0, 1, 0, -2, -1, -1, 0, 2, 1, 1, 1, -2, 0, 1, -1, -1, 2, 1, -1, 1, 0, -2, -1, 0, -1, 0, 3, 1, -1, 1, 1, -3, -2, 1, -1, -1, 2, 1, -1, 1, 0, -3, -1, 2, 1, -1, 0, 4, 2, -1, -1, 1, 1, -3, -1, 2, 0, -1, -1, 3, 1, -3, -1, 1, 0, -4, -2, 2, 1, -1, 0, 4, 2, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,23

COMMENTS

Row sums equal A003406 (offset 1), the expansion of Ramanujan's function: R(x) = 1 + Sum_{n>=1} { x^(n*(n+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^n)) }.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

G.f. of column k: x^(k*(k+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^k)) for k>=1.

EXAMPLE

Triangle begins:

1;

-1;

1, 1;

-1,-1;

1, 0;

-1, 0, 1;

1, 1,-1;

-1,-1, 0;

1, 0,-1;

-1, 0, 2, 1;

1, 1,-1,-1;

-1,-1, 1, 0;

1, 0,-2,-1;

-1, 0, 2, 1;

1, 1,-2, 0, 1;

-1,-1, 2, 1,-1;

1, 0,-2,-1, 0;

-1, 0, 3, 1,-1;

1, 1,-3,-2, 1;

-1,-1, 2, 1,-1;

PROG

(PARI) {T(n, k)=if(n<k|k<1, 0, if(n==1, 1, T(n-k, k-1)-T(n-k, k)))}

CROSSREFS

Cf. A003406, A008289.

Sequence in context: A056980 A268643 A005094 * A338639 A249351 A123706

Adjacent sequences:  A121369 A121370 A121371 * A121373 A121374 A121375

KEYWORD

sign,tabf

AUTHOR

Paul D. Hanna, Jul 24 2006

STATUS

approved

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)