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.

A185755 Triangle: T(n,k) equals the coefficient of x^n*y^k in the n-th iteration of x*(1+xy)/(1-x), for n>=1, 0<=k

Original entry on oeis.org

1, 2, 2, 9, 15, 6, 64, 154, 120, 30, 625, 1995, 2340, 1190, 220, 7776, 31191, 49315, 38325, 14595, 2170, 117649, 571221, 1142932, 1204588, 704102, 215950, 27076, 2097152, 11992688, 29141994, 38972388, 30945432, 14570976, 3761310, 409836
Offset: 1

Views

Author

Paul D. Hanna, Feb 03 2011

Keywords

Examples

			Triangle begins:
1;
2, 2;
9, 15, 6;
64, 154, 120, 30;
625, 1995, 2340, 1190, 220;
7776, 31191, 49315, 38325, 14595, 2170;
117649, 571221, 1142932, 1204588, 704102, 215950, 27076;
2097152, 11992688, 29141994, 38972388, 30945432, 14570976, 3761310, 409836;
43046721, 283976517, 814059798, 1323693384, 1334427720, 853356072, 337738758, 75550188, 7303164; ...

Crossrefs

Cf. columns: A000169, A185756, A185757; row sums: A185523.
Cf. diagonals: A112317, A185758, A185759.

Programs

  • PARI
    {T(n,k)=local(A=x, G=x*(1+x*y)/(1-x)); for(i=1, n, A=subst(G, x, A+x*O(x^n)));polcoeff(polcoeff(A, n,x),k,y)}

Formula

T(n,0) = A000169(n) = n^(n-1).
T(n,n) = A112317(n).
Sum_{k=0..n-1} T(n,k) = A185523(n).
Sum_{k=0..n-1} (-1)^k*T(n,k) = 0^n.

A185756 Column 1 of triangle A185755.

Original entry on oeis.org

2, 15, 154, 1995, 31191, 571221, 11992688, 283976517, 7487521975, 217567092743, 6907888374828, 237951469523807, 8838510559556783, 352160268261051113, 14982705940607112640, 677935029521206050505, 32508195354031791206799
Offset: 1

Views

Author

Paul D. Hanna, Feb 03 2011

Keywords

Comments

Column 0 of triangle A185755 equals n^(n-1).
A185755(n,k) equals the coefficient of x^n*y^k in the n-th iteration of x*(1+xy)/(1-x).

Crossrefs

Cf. A185755, A185757, A185758, A185759.

A185757 Column 2 of triangle A185755.

Original entry on oeis.org

6, 120, 2340, 49315, 1142932, 29141994, 814059798, 24779916843, 817506518829, 29081010732059, 1110248649302494, 45298134089851175, 1967550159430960784, 90668183653348456484, 4418855084158930131012, 227122154996245283660487
Offset: 1

Views

Author

Paul D. Hanna, Feb 03 2011

Keywords

Comments

A185755(n,k) equals the coefficient of x^n*y^k in the n-th iteration of x*(1+xy)/(1-x).

Crossrefs

Cf. A185755, A185756, A185758, A185759.

A185758 A diagonal of triangle A185755.

Original entry on oeis.org

2, 15, 120, 1190, 14595, 215950, 3761310, 75550188, 1721103648, 43872089118, 1237592664451, 38282002057156, 1288537309627464, 46886217384094764, 1834003542264708444, 76744318019878844916, 3420833746251201921980
Offset: 1

Views

Author

Paul D. Hanna, Feb 03 2011

Keywords

Comments

A185755(n,k) equals the coefficient of x^n*y^k in the n-th iteration of x*(1+xy)/(1-x).

Crossrefs

Cf. A185755, A185756, A185757, A185759.

Programs

  • PARI
    {a(n)=local(A=x, G=x*(1+x*y)/(1-x)); for(i=1, n+1, A=subst(G, x, A+O(x^(n+2))));polcoeff(polcoeff(A, n+1,x),n-1,y)}
Showing 1-4 of 4 results.

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

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