cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A137156 Matrix inverse of triangle A137153(n,k) = C(2^k+n-k-1, n-k), read by rows.

Original entry on oeis.org

1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 9, -24, 22, -8, 1, -88, 239, -228, 92, -16, 1, 1802, -4920, 4749, -1976, 376, -32, 1, -75598, 206727, -200240, 84086, -16432, 1520, -64, 1, 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1
Offset: 0

Views

Author

Paul D. Hanna, Jan 24 2008

Keywords

Comments

Unsigned column 0 = A001192, number of full sets of size n.

Examples

			Triangle begins:
        1;
       -1,         1;
        1,        -2,        1;
       -2,         5,       -4,        1;
        9,       -24,       22,       -8,       1;
      -88,       239,     -228,       92,     -16,       1;
     1802,     -4920,     4749,    -1976,     376,     -32,    1;
   -75598,    206727,  -200240,    84086,  -16432,    1520,  -64,    1;
  6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1;
  ...

Crossrefs

Cf. A137153 (matrix inverse); unsigned columns: A001192, A137157, A137158, A137159; unsigned row sums: A137160.

Programs

  • PARI
    /* As matrix inverse of A137153: */
{T(n,k) = local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(2^(c-1)+r-c-1,r-c)))); if(n
  • PARI
    /* Using the g.f.: */
{T(n,k) = if(n

Formula

G.f. of column k: 1 = Sum_{n>=0} T(n+k,k)*x^n/(1-x)^(2^(n+k)).

A137157 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1+x)^(2*2^n).

Original entry on oeis.org

1, 2, 5, 24, 239, 4920, 206727, 17568408, 3003763243, 1030272816360, 707851744149198, 973425618916674288, 2678332881795756783639, 14741522294008025924154864, 162290544340043699103996962253, 3573515596966915773419766367302288, 157376160486791180710467411977740266927
Offset: 0

Views

Author

Paul D. Hanna, Jan 24 2008

Keywords

Comments

Equals unsigned column 1 of triangle A137156.

Crossrefs

Cf. A137156; A001192, A137158, A137159, A137160.

Programs

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

Extensions

a(15)-a(16) from Alois P. Heinz, Jan 04 2023

A137159 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1+x)^(8*2^n).

Original entry on oeis.org

1, 8, 92, 1976, 84086, 7173240, 1227862380, 421296930984, 289484024512093, 398106386971472608, 1095381029276651137560, 6028986377761538637043792, 66373632185586959347740452492, 1461497816340787260620205149915824
Offset: 0

Views

Author

Paul D. Hanna, Jan 24 2008

Keywords

Comments

Equals unsigned column 3 of triangle A137156.

Crossrefs

Cf. A137156; A001192, A137157, A137158, A137160.

Programs

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

A137160 G.f.: 1 = Sum_{n>=0} a(n)*x^n*(1-x)/(1+x)^(2^n).

Original entry on oeis.org

1, 2, 4, 12, 64, 664, 13856, 584668, 49751520, 8509625760, 2919099754336, 2005648412219832, 2758163973596156000, 7588978611071894509464, 41769719229784446295570112, 459846172005153447271276789620
Offset: 0

Views

Author

Paul D. Hanna, Jan 24 2008

Keywords

Comments

Equals the unsigned row sums of triangle A137156.

Crossrefs

Cf. A137156; A001192, A137157, A137158, A137159.

Programs

  • PARI
    {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x)/(1+x+x*O(x^n))^(2^k) ), n)}
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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