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A185786 Third accumulation array of A107985, by antidiagonals. 2
1, 6, 6, 21, 35, 21, 56, 120, 120, 56, 126, 315, 405, 315, 126, 252, 700, 1050, 1050, 700, 252, 462, 1386, 2310, 2695, 2310, 1386, 462, 792, 2520, 4536, 5880, 5880, 4536, 2520, 792, 1287, 4290, 8190, 11466, 12740, 11466, 8190, 4290, 1287, 2002, 6930, 13860, 20580, 24696, 24696, 20580, 13860, 6930, 2002, 3003, 10725, 22275, 34650 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A185784. The pattern established by the formulas for A185785, A185786, A185787, suggests that the H-th accumulation array of A107985 may be given by

  T(n,k)=(n+k+H)C(n+H,H+1)C(k+H,H+1)/(H+2).

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(n,k) = (n+k+3)*C(n+3,4)*C(k+3,4)/5.

EXAMPLE

Northwest corner:

1....6.....21.....56.....126

6....35....120....315....700

21...120...405....1050...2310

56...315...1050...2695...5880

MATHEMATICA

(See A185784.)

f[n_, k_] := Binomial[k + 3, 4]*Binomial[n + 3, 4]*(n + k + 3)/5; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

CROSSREFS

Cf. A185784.

Sequence in context: A198340 A189980 A188273 * A178822 A253069 A255460

Adjacent sequences:  A185783 A185784 A185785 * A185787 A185788 A185789

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 03 2011

STATUS

approved

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Last modified November 18 17:57 EST 2019. Contains 329288 sequences. (Running on oeis4.)