login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110814 Inverse of a triangle of pyramidal numbers. 2
1, -3, 1, 7, -4, 1, -15, 11, -5, 1, 31, -26, 16, -6, 1, -63, 57, -42, 22, -7, 1, 127, -120, 99, -64, 29, -8, 1, -255, 247, -219, 163, -93, 37, -9, 1, 511, -502, 466, -382, 256, -130, 46, -10, 1, -1023, 1013, -968, 848, -638, 386, -176, 56, -11, 1, 2047, -2036, 1981, -1816, 1486, -1024, 562, -232, 67, -12, 1, -4095, 4083 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inverse of A110813. Array factors as (1/(1+2x),x)*(1/(1+x),x/(1+x)). Row sums are (-2)^n. Diagonal sums are (-1)^n*A008466(n+2). Signed version of A104709.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

Number triangle T(n, k) = Sum_{j=0..n} (-2)^(n-j)*binomial(j, k)*(-1)^(j-k).

Riordan array (1/(1+3x+2x^2), x/(1+x)).

T(n,k) = -3*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k) + 2*T(n-2,k-1), T(0,0)=1, T(n,k)=0 if k < 0 or if k > n. - Philippe Deléham, Nov 30 2013

EXAMPLE

Rows begin

    1;

   -3,   1;

    7,  -4,   1;

  -15,  11,  -5,   1;

   31, -26,  16,  -6,   1;

MAPLE

A110814_row := proc(n) add((-1)^k*add(binomial(n, n-i)*x^(n-k-1), i=0..k), k=0..n-1); coeffs(sort(%)) end; seq(print(A110814_row(n)), n=1..6); # Peter Luschny, Sep 29 2011

MATHEMATICA

T[n_, k_] := Sum[(-2)^(n - j)*Binomial[j, k]*(-1)^(j - k), {j, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 19 2017 *)

PROG

(PARI) for(n=0, 10, for(k=0, n, print1(sum(j=0, n, (-2)^(n-j)*(-1)^(j-k)* binomial(j, k)), ", "))) \\ G. C. Greubel, Oct 19 2017 *)

CROSSREFS

Sequence in context: A323956 A086272 A104709 * A275599 A210038 A319076

Adjacent sequences:  A110811 A110812 A110813 * A110815 A110816 A110817

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Aug 05 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 17:07 EDT 2019. Contains 324196 sequences. (Running on oeis4.)