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A198060 Array read by antidiagonals, m>=0, n>=0, A(m,n) = sum{k=0..n} sum{j=0..m} sum{i=0..m} (-1)^(j+i)*C(i,j)*C(n,k)^(m+1)*(n+1)^j*(k+1)^(m-j)/(k+1)^m. 10
1, 1, 2, 1, 3, 4, 1, 4, 10, 8, 1, 5, 22, 35, 16, 1, 6, 46, 134, 126, 32, 1, 7, 94, 485, 866, 462, 64, 1, 8, 190, 1700, 5626, 5812, 1716, 128, 1, 9, 382, 5831, 35466, 69062, 40048, 6435, 256, 1, 10, 766, 19682, 219626, 795312, 882540, 281374, 24310, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

FORMULA

A198060(n,2) = A033484(n+1).

EXAMPLE

m\n  [0] [1]  [2]   [3]     [4]     [5]        [6]

--------------------------------------------------

[0]   1   2    4     8      16       32         64   A000079

[1]   1   3   10    35     126      462       1716   A001700

[2]   1   4   22   134     866     5812      40048   A197657

[3]   1   5   46   485    5626    69062     882540   A198256

[4]   1   6   94  1700   35466   795312   18848992   A198257

[5]   1   7  190  5831  219626  8976562  394800204   A198258

MAPLE

A198060 := proc(m, n) local i, j, k, pow;

pow := (a, b) -> if a=0 and b=0 then 1 else a^b fi;

add(add(add((-1)^(j+i)*binomial(i, j)*binomial(n, k)^(m+1)*pow(n+1, j)*pow(k+1, m-j)/(k+1)^m, i=0..m), j=0..m), k=0..n) end:

for m from 0 to 6 do seq(A198060(m, n), n=0..6) od;

MATHEMATICA

a[m_, n_] := Sum[ Sum[ Sum[(-1)^(j + i)*Binomial[i, j]*Binomial[n, k]^(m+1)*(n+1)^j*(k+1)^(m-j)/(k+1)^m, {i, 0, m}], {j, 0, m}], {k, 0, n}]; Table[ a[m-n, n], {m, 0, 9}, {n, 0, m}] // Flatten (* Jean-Fran├žois Alcover, Jun 27 2013 *)

CROSSREFS

Cf. A198061.

Sequence in context: A104711 A133112 A247239 * A327084 A159856 A137649

Adjacent sequences:  A198057 A198058 A198059 * A198061 A198062 A198063

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Nov 01 2011

STATUS

approved

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Last modified August 8 11:12 EDT 2020. Contains 336293 sequences. (Running on oeis4.)