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 1-3 of 3 results.

A061315 Array read by antidiagonals: T(n,k)=T(n,k-1)*(T(n,k-1)+k-1)/k with T(n,1)=n.

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 1, 5, 6, 4, 1, 10, 16, 10, 5, 1, 28, 76, 40, 15, 6, 1, 154, 1216, 430, 85, 21, 7, 1, 3520, 247456, 37324, 1870, 161, 28, 8, 1, 1551880
Offset: 1

Views

Author

Henry Bottomley, Apr 24 2001

Keywords

Comments

Not always an integer

Examples

			1,1,1,1,1,1,1,1,1,1,...
2,3,5,10,28,154,3520,1551880,267593772160,7160642690122633501504,...
3,6,16,76,1216,247456,61235956672/7,468730299066952899064/49,...
4,10,40,430,37324,232211266,7703153350084336,7417321441864447837991470393906,
5,15,85,1870,700876,81871778626,957569733696568731376,...
6,21,161,6601,8719921,12672844307641,22942997549397847673832961,...
7,28,280,19810,78503068,1027122012987994,...

Crossrefs

Rows include A000012 and A003504. Columns include A000027, A000217, A006007, A061319 and A061321.

Formula

a(n) =A061314(n, k-1)/k

A061318 Column 3 of A061314.

Original entry on oeis.org

0, 4, 40, 304, 1720, 7480, 26404, 79240, 209304, 499140, 1095160, 2242504, 4332640, 7966504, 14036260, 23829040, 39156304, 62512740, 97268904, 147902080, 220270120, 321933304, 462529540, 654208504, 912130600, 1255036900, 1705896504, 2292638040, 3048972304, 4015313320
Offset: 0

Views

Author

Henry Bottomley, Apr 24 2001

Keywords

Links

Crossrefs

Cf. A006007, A061314, A061316, A061319.

Programs

  • Mathematica
    CoefficientList[Series[-4x (1+x+22x^2+22x^3+22x^4+x^5+x^6)/(x-1)^9,{x,0,30}],x] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,4,40,304,1720,7480,26404,79240,209304},30] (* Harvey P. Dale, Jul 04 2023 *)

Formula

a(n) = A061316(n) + A006007(n)^2 = 4*A061319(n).
G.f. -4*x*(1+x+22*x^2+22*x^3+22*x^4+x^5+x^6)/(x-1)^9. - R. J. Mathar, Aug 11 2012

Extensions

a(25)-a(29) from Stefano Spezia, Aug 31 2023

A061320 Column 4 of A061314.

Original entry on oeis.org

0, 5, 140, 6080, 186620, 3504380, 43599605, 392515340, 2738219580, 15571795365, 74962059260, 314303754380, 1173239918240, 3966582090380, 12313551210485, 35488970536640, 95826048090080, 244240228906965, 591327577603980, 1367189227172480, 3032433080571020
Offset: 0

Views

Author

Henry Bottomley, Apr 24 2001

Keywords

Crossrefs

Cf. A061314, A061318, A061319, A061321.

Formula

a(n) = A061318(n) + A061319(n)^2 = 5*A061321(n).
G.f.: -5*x*(1 +11*x +876*x^2 +19780*x^3 +215084*x^4 +1114665*x^5 +2936419*x^6 +4038928*x^7 +2936419*x^8 +1114665*x^9 +215084*x^10 +19780*x^11 +876*x^12 +11*x^13+x^14) / (x-1)^17. - R. J. Mathar, Aug 11 2012
a(n) = n *(n+1) *(n^8+4*n^7+14*n^6+28*n^5+77*n^4+112*n^3+196*n^2+144*n+2304) *(n^2+n+4) * (n^4+2*n^3+5*n^2+4*n+36)/331776. - R. J. Mathar, Aug 11 2012
Showing 1-3 of 3 results.

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

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