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.

A141761 Column 0 of triangle A141760.

Original entry on oeis.org

1, 1, 1, 2, 6, 26, 154, 1188, 11474, 134432, 1863168, 29936846, 548625820, 11315025894, 259733293774, 6574304470320, 182050022755386, 5477819548007438, 178054691097463354, 6220193033111607018
Offset: 0

Views

Author

Paul D. Hanna, Jul 18 2008

Keywords

Comments

Also equals column 1 (shifted) of triangle A141760.

Crossrefs

Cf. A141760, A141762, A141763, A141764.

Programs

  • PARI
    {a(n)=if(n==0,1,1 - sum(j=0,n-1,a(j)*(-1)^(n-j)*binomial(j*(j-1)/2+n-j-1,n-j)))}

Formula

G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1+x)^{n*(n-1)/2}.
a(n) = 1 - Sum_{j=0..n-1} a(j) * (-1)^(n-j) * C(j(j-1)/2 + n-j-1, n-j) for n>0, with a(0)=1.

A141762 Column 2 of triangle A141760.

Original entry on oeis.org

1, 1, 3, 13, 77, 594, 5737, 67216, 931584, 14968423, 274312910, 5657512947, 129866646887, 3287152235160, 91025011377693, 2738909774003719, 89027345548731677, 3110096516555803509, 116244489639439112395
Offset: 0

Views

Author

Paul D. Hanna, Jul 18 2008

Keywords

Crossrefs

Cf. A141760, A141761, A141763, A141764.

Programs

  • PARI
    {a(n)=if(n==0,1,1 - sum(j=0,n-1,a(j)*(-1)^(n-j)*binomial((j+1)*(j+2)/2-1+n-j-1,n-j)))}

Formula

G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1+x)^[(n+1)*(n+2)/2 - 1].
a(n) = 1 - Sum_{j=0..n-1} a(j) * (-1)^(n-j) * C((j+1)(j+2)/2 + n-j-2, n-j) for n>0, with a(0)=1.

A141763 Column 3 of triangle A141760.

Original entry on oeis.org

1, 1, 4, 23, 175, 1678, 19579, 270683, 4342447, 79498622, 1638471038, 37592670383, 951214496814, 26333793485772, 792232525678756, 25747819699179668, 899388184082559576, 33613386298645020835, 1338749843351681925409
Offset: 0

Views

Author

Paul D. Hanna, Jul 18 2008

Keywords

Crossrefs

Cf. A141760, A141761, A141762, A141764.

Programs

  • PARI
    {a(n)=if(n==0,1,1 - sum(j=0,n-1,a(j)*(-1)^(n-j)*binomial((j+2)*(j+3)/2-3+n-j-1,n-j)))}

Formula

G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1+x)^{(n+2)*(n+3)/2 - 3}.
a(n) = 1 - Sum_{j=0..n-1} a(j) * (-1)^(n-j) * C((j+2)(j+3)/2 + n-j-4, n-j) for n>0, with a(0)=1.

A141764 Column 4 of triangle A141760.

Original entry on oeis.org

1, 1, 5, 36, 336, 3863, 52944, 844777, 15411547, 316888806, 7258887646, 183464090374, 5074934980977, 152584140132667, 4956824851572271, 173086933804868142, 6467223731119047195, 257524741272166890188
Offset: 0

Views

Author

Paul D. Hanna, Jul 18 2008

Keywords

Crossrefs

Cf. A141760, A141761, A141762, A141763.

Programs

  • PARI
    {a(n)=if(n==0,1,1 - sum(j=0,n-1,a(j)*(-1)^(n-j)*binomial((j+3)*(j+4)/2-6+n-j-1,n-j)))}

Formula

G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1+x)^{(n+3)*(n+4)/2 - 6}.
a(n) = 1 - Sum_{j=0..n-1} a(j) * (-1)^(n-j) * C((j+3)(j+4)/2 + n-j-7, n-j) for n>0, with a(0)=1.
Showing 1-4 of 4 results.

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

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