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.

A060075 Third column of triangle A060074.

Original entry on oeis.org

1, 14, 331, 12284, 663061, 49164554, 4798037791, 596372040824, 91991577140521, 17244625801225094, 3861296322290987251, 1017889493782391701364, 312043142223584185393981, 110072908401904868672053634, 44269461921572566583027776711, 20136444961077089693182895665904
Offset: 0

Views

Author

Wolfdieter Lang, Mar 16 2001

Keywords

Comments

Also third diagonal of triangle A060058.
a(n) is n-fold iterated sum of squares with last upper summation index 3 and other upper summation indices j[k]+1, k=2,...,n. See Comments A060061 for the threefold iteration with last upper summation index n.

Crossrefs

Cf. A000364, A060058, A060061, A060074.

Programs

  • Mathematica
    a[n_] := (Abs[EulerE[2*n+2]] - Abs[EulerE[2*n]]) / 4; Array[a, 16] (* Amiram Eldar, May 03 2025 *)
  • PARI
    a(n) = (abs(eulerfrac(2*n+2)) - abs(eulerfrac(2*n))) / 4; \\ Amiram Eldar, May 03 2025

Formula

a(n) = A060074(n+2, 2) = A060058(2+n, n).
a(n) = (1/4)*(A000364(n+1) - A000364(n)). - Benoit Cloitre, Apr 06 2003
G.f.: sin(x)^2/cos(x)^3 = x^2/2! + 14*x^4/4! + 331*x^6/6! + ... - Peter Bala, Oct 22 2019

A060062 Fifth column of triangle A060058.

Original entry on oeis.org

1385, 50521, 663061, 5162421, 28862471, 127838711, 475638163, 1544454483, 4494470838, 11949575638, 29449955678, 68035028126, 148639284066, 309297261826, 616573557226, 1183184394986, 2194487337735, 3947417571735, 6906579371835, 11783600663835, 19647572529585
Offset: 0

Views

Author

Wolfdieter Lang, Mar 16 2001

Keywords

Comments

Fourfold iterated sums of squares; see A060061 for threefold case.

Links

Programs

  • Mathematica
    CoefficientList[Series[(1385+32516*x+114318*x^2+87156*x^3+11025*x^4)/(1-x)^13 ,{x,0,20}],x] (* Indranil Ghosh, Feb 21 2017 *)

Formula

G.f. (1385+32516*x+114318*x^2+87156*x^3+11025*x^4)/(1-x)^13 = p(4, x)/(1-x)^(4*3+1) with p(2, x)=sum(A060063(4, m)*x^m, m=0..4).

A060076 Fourth column of triangle A060074.

Original entry on oeis.org

1, 30, 1211, 68060, 5162421, 510964090, 64108947631, 9954077496120, 1874917179220841, 421327494210872150, 111374995513203846051, 34217341079365673500180, 12091183195611248756287261
Offset: 0

Views

Author

Wolfdieter Lang, Mar 16 2001

Keywords

Comments

Also fourth diagonal of triangle A060058.
a(n) is n-fold iterated sum of squares with last upper summation index 4 and other upper summation indices j[k]+1, k=2,...,n. See Comments A060061 for the threefold iteration with last upper summation index n.

Formula

a(n)=A060074(n+3, 3)= A060058(3+n, n).

A060077 Fifth column of triangle A060074.

Original entry on oeis.org

1, 55, 3486, 281210, 28862471, 3706931865, 584856590956, 111432850130020, 25255179275602941, 6719606199432053675, 2074965724098955112426, 736196253336729035680830, 297480985088238886530733411
Offset: 0

Views

Author

Wolfdieter Lang, Mar 16 2001

Keywords

Comments

Also fifth diagonal of triangle A060058.
a(n) is n-fold iterated sum of squares with last upper summation index 5 and other upper summation indices j[k]+1, k=2,...,n. See Comments A060061 for the threefold iteration with last upper summation index n.

Crossrefs

Cf. A060058, A060061, A060074.

Formula

a(n) = A060074(n+4, 4) = A060058(4+n, n).

A060078 Sixth column of triangle A060074.

Original entry on oeis.org

1, 91, 8526, 948002, 127838711, 20829905733, 4059150905356, 935210483855284, 251931148208847261, 78543629143430050655, 28079156490294534487226, 11415592075705105510977846, 5238681589930616835789832051
Offset: 0

Views

Author

Wolfdieter Lang, Mar 16 2001

Keywords

Comments

Also sixth diagonal of triangle A060058.
a(n) is n-fold iterated sum of squares with last upper summation index 6 and other upper summation indices j[k]+1, k=2,...,n. See Comments A060061 for the threefold iteration with last upper summation index n.
Showing 1-5 of 5 results.

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