The On-Line Encyclopedia of Integer Sequences (OEIS)

A156539 revision #3

A156539

A recursion triangle sequence:f(q,k)=(1 - (-q)^k)/(1 + q);q=2; e(n,k)= f(q, k + n - 1)*e(n - 1, k) + (-q)^(n + k - 2)e(n - 1, k - 1).

1, 1, 1, 1, -13, 1, 1, -127, 395, 1, 1, 2635, 8857, -50645, 1, 1, 113369, -1090125, -6392903, 25929899, 1, 1, -9636493, -157388911, 2738123923, 11163788345, -53104434517, 1, 1, -1647840047, 58603503067, 1708972394545, -20846248885229

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OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, -11, 270, -39151, 18560242, -39369547651, 316649873125334,

-10469504736950236343, 1366047251880111590518042,...}.

The recursion sequence is an effort to get the q-Lah recursion.

LINKS

Table of n, a(n) for n=1..33.

R. Parthasarathy, q-Fermionic Numbers and Their Roles in Some Physical Problems, arxiv:quant-ph/0403216

FORMULA

f(q,k)=(1 - (-q)^k)/(1 + q);q=2;;

e(n,k)= f(q, k + n - 1)*e(n - 1, k) + (-q)^(n + k - 2)e(n - 1, k - 1).

EXAMPLE

{1},

{1, 1},

{1, -13, 1},

{1, -127, 395, 1},

{1, 2635, 8857, -50645, 1},

{1, 113369, -1090125, -6392903, 25929899, 1},

{1, -9636493, -157388911, 2738123923, 11163788345, -53104434517, 1},

{1, -1647840047, 58603503067, 1708972394545, -20846248885229, -99301333604807, 435031527557803, 1},

{1, 561913455515, 38338804386633, -2452767292835141, -49931154777504079, 713057053683646995, 3124896325732724281, -14255113095014110549, 1},

{1, 383786890117769, -53483266744648765, -6541471733965121303, 292767105902855250491, 6970650157511849296049, -91628813770737106650605, -418026940631041685516743, 1868446183589689497791147, 1}

MATHEMATICA

Clear[e, n, k, q]; f[q_, k_] := (1 - (-q)^k)/(1 + q);

q = 2; e[n_, 0] := 0; e[n_, 1] := 1;

e[n_, n_] := 1; e[n_, k_] := 0 /; k >= n + 1;

e[n_, k_] := f[q, k + n - 1]*e[n - 1, k] + (-q)^(n + k - 2)e[n - 1, k - 1];

Table[Table[e[n, k], {k, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A174694 A353952 A340432 * * A172300 A022176

Adjacent sequences: A156536 A156537 A156538 * A156540 A156541 A156542

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 09 2009

STATUS

editing