A061321 -id:A061321 - cp's OEIS frontend

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

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

Henry Bottomley, Apr 24 2001

Not always an integer

			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,...

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

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

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

Henry Bottomley, Apr 24 2001

Cf. A061314, A061318, A061319, A061321.

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

cp's OEIS Frontend

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

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