A061320 -id:A061320 - cp's OEIS frontend

A061314 Table read by descending antidiagonals where T(n,k) = T(n,k-1) + T(n,k-1)^2/k^2 and T(n,0)=n.

0, 0, 1, 0, 2, 2, 0, 3, 6, 3, 0, 4, 15, 12, 4, 0, 5, 40, 48, 20, 5, 0, 6, 140, 304, 120, 30, 6, 0, 7, 924, 6080, 1720, 255, 42, 7, 0, 8, 24640, 1484736, 186620, 7480, 483, 56, 8, 0, 9, 12415040, 61235956672, 1393267596, 3504380, 26404, 840, 72, 9, 0, 10

Offset: 0

Henry Bottomley, Apr 24 2001

Not always an integer.

			The table begins:
    0,       0,       0,       0,          0,...
    1,       2,       3,       4,          5,...
    2,       6,      15,      40,        140,...
    3,      12,      48,     304,       6080,...
    4,      20,     120,    1720,     186620,...
    5,      30,     255,    7480,    3504380,...
    6,      42,     483,   26404,   43599605,...
    7,      56,     840,   79240,  392515340,...
    8,      72,    1368,  209304, 2738219580,...
    ...

Rows include A000004, A000027 and A061322. Columns include A001477, A002378, A061316, A061318 and A061320.

T(n, k) = T(n, k-1) + A061315(n, k)^2.

A061319 Column 4 of A061315.

Original entry on oeis.org

0, 1, 10, 76, 430, 1870, 6601, 19810, 52326, 124785, 273790, 560626, 1083160, 1991626, 3509065, 5957260, 9789076, 15628185, 24317226, 36975520, 55067530, 80483326, 115632385, 163552126, 228032650, 313759225, 426474126, 573159510

Offset: 0

Henry Bottomley, Apr 24 2001

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

a(n) =A061318(n)/4 =sqrt(A061320(n)-A061318(n)).
G.f. -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
a(n) = n*(n+1)*(n^2+n+4)*(n^4+2*n^3+5*n^2+4*n+36)/576 . R. J. Mathar, Aug 11 2012

A061321 Column 5 of A061315.

Original entry on oeis.org

0, 1, 28, 1216, 37324, 700876, 8719921, 78503068, 547643916, 3114359073, 14992411852, 62860750876, 234647983648, 793316418076

Offset: 0

Henry Bottomley, Apr 24 2001

nonn

a(n) =A061320(n)/5.

cp's OEIS Frontend

A061314 Table read by descending antidiagonals where T(n,k) = T(n,k-1) + T(n,k-1)^2/k^2 and T(n,0)=n.

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A061319 Column 4 of A061315.

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A061321 Column 5 of A061315.

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