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 1-5 of 5 results.

A060345 An expansion related to Yukawa coupling.

Original entry on oeis.org

5, 2875, 4876875, 8564575000, 15517926796875, 28663236110956000, 53621944306062201000, 101216230345800061125625, 192323666400003538944396875, 367299732093982242625847031250, 704288164978454714776724365580000, 1354842473951260627644461070753075500, 2613295702542192770504516764304958585000
Offset: 0

Views

Author

N. J. A. Sloane, Mar 30 2001

Keywords

Comments

Coefficients of 3-point function in dimension 3 [Morrison].

Examples

			a(10) = A060041(1) + 8*A060041(2) + 125*A060041(5) + 1000*A060041(10) = 704288164978454714776724365580000.
		

Crossrefs

Programs

  • PARI
    cumsum(v) = for(i=2, #v, v[i] += v[i-1]); v;
    seq(N, {d=5}) = {
      my(x = 'x + O('x^(N+1)), h = cumsum(vector(d*N, n, 1/n)),
         y0 = sum(n=0, N, (d*n)!/n!^d * x^n),
         y1 = d * sum(n = 1, N, ((d*n)!/n!^d * (h[d*n] - h[n])) * x^n),
         Qx = x * exp(y1/y0), Xq = serreverse(Qx));
      Vec(d * (x * Xq'/Xq)^(d-2) / ((1 - d^d*Xq) * sqr(subst(y0, 'x, Xq))));
    };
    seq(20)  \\ Gheorghe Coserea, Jul 29 2016

Formula

Sum_{n >= 0} a(n)*q^n = 5 + Sum_{n >= 1} A060041(n)*n^3*q^n/(1-q^n).

Extensions

More terms from Vladeta Jovovic, Apr 01 2001
a(6) corrected and a(10)-a(12) added by Gheorghe Coserea, Jul 28 2016

A076910 Coefficients of 5-point function in dimension 5.

Original entry on oeis.org

7, 3727381, 2637885990187, 1927092954108108787, 1425153551321014327663291, 1060347883438857662557634869906, 791661306374088776109692880989252173, 592348256908461616176898022359492565546566, 443865568545713063761643598030194801299861575595, 332947403131697202086626568381790256001850741509664373
Offset: 0

Views

Author

N. J. A. Sloane, Nov 28 2002

Keywords

Crossrefs

Extensions

a(7)-a(9) from Greene et al. added by Andrey Zabolotskiy, Sep 11 2022

A076911 Coefficients of 6-point function in dimension 6.

Original entry on oeis.org

8, 106975232, 1672023727001600, 26611692333081695092736, 426129121674687823674948571136, 6842148599241293047857339542861643776, 110018992594692024449889564415904439556898816, 1770551943055574073245974844490813198478975912902656, 28508925683951911989843155602330000507452539542539447947264
Offset: 0

Views

Author

N. J. A. Sloane, Nov 28 2002

Keywords

Crossrefs

Extensions

a(6)-a(8) from Greene et al. added by Andrey Zabolotskiy, Sep 11 2022

A076913 Coefficients of 3-point function in dimension 4.

Original entry on oeis.org

6, 60480, 440884080, 6255156277440, 117715791990353760, 2591176156368821985600
Offset: 0

Views

Author

N. J. A. Sloane, Nov 28 2002

Keywords

Comments

Klemm and Pandharipande's Table 2 contains the sequence that agrees with the initial terms given here, a(1)-a(5). It continues 63022367592536650014764880, 1642558496795158117310144372160, 45038918271966862868230872208340160. - Andrey Zabolotskiy, Sep 11 2022

Crossrefs

A076915 Coefficients of 3-point function in dimension 5 Y^1_2.

Original entry on oeis.org

7, 1707797, 510787745643, 222548537108926490, 113635631482486991647224
Offset: 0

Views

Author

N. J. A. Sloane, Nov 28 2002

Keywords

Comments

Zinger's paper contains the sequence that agrees with the initial terms given here, a(1)-a(4). It continues: 63340724462384110502639024265, 37325795060717360046547665187418254, 22857028298936684292245509537579343818647, 14395953469762596243721601709186933042635134584, 9263611884884554518268724722981763557936573405648178, 6062677702410680024315392235188823274104219383883410807999. - Andrey Zabolotskiy, Sep 11 2022

Crossrefs

Extensions

Name corrected by Andrey Zabolotskiy, May 13 2020
Showing 1-5 of 5 results.