A275331 Triangle read by rows, T(n,k) = k*Sum_{m=1..n/k} t(k)*t(n-k*m+1) with t = A000081, for n>=1 and 1<=k<=n.

1, 2, 2, 4, 2, 6, 8, 6, 6, 16, 17, 10, 12, 16, 45, 37, 24, 30, 32, 45, 120, 85, 50, 60, 64, 90, 120, 336, 200, 120, 132, 160, 180, 240, 336, 920, 486, 280, 318, 336, 405, 480, 672, 920, 2574, 1205, 692, 750, 800, 945, 1080, 1344, 1840, 2574, 7190

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Example

Triangle starts:
[n] [k=1,2,...] row sum
[1] [1] 1
[2] [2, 2] 4
[3] [4, 2, 6] 12
[4] [8, 6, 6, 16] 36
[5] [17, 10, 12, 16, 45] 100
[6] [37, 24, 30, 32, 45, 120] 288
[7] [85, 50, 60, 64, 90, 120, 336] 805
[8] [200, 120, 132, 160, 180, 240, 336, 920] 2288
[9] [486, 280, 318, 336, 405, 480, 672, 920, 2574] 6471

Prog

(Sage)
@cached_function
def t():
    n = 1
    b = [0, 1]
    while True:
        S = [k*sum(b[k]*b[n-k*m+1] for m in (1..n//k)) for k in (1..n)]
        b.append(sum(S)//n)
        yield S
        n += 1
t_list = t()
for n in (1..8): print(next(t_list))

Crossrefs

T(n,0) = A087803(n).

T(n,n) = A055544(n).

Sum_k T(n,k) = A095350(n+1).

Cf. A000081, A275330.

Sequence in context: A307536 A248842 A286538 * A308828 A325683 A331121

Adjacent sequences: A275328 A275329 A275330 * A275332 A275333 A275334

Keyword

nonn,tabl

Author

Peter Luschny, Aug 18 2016

Status

approved