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A275330 Triangle read by rows, T(n,k) = t(n-k+1)*Sum_{d|k} d*t(d) with t = A000081, for n>=1 and 1<=k<=n. 1
1, 1, 3, 2, 3, 7, 4, 6, 7, 19, 9, 12, 14, 19, 46, 20, 27, 28, 38, 46, 129, 48, 60, 63, 76, 92, 129, 337, 115, 144, 140, 171, 184, 258, 337, 939, 286, 345, 336, 380, 414, 516, 674, 939, 2581, 719, 858, 805, 912, 920, 1161, 1348, 1878, 2581, 7238 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

EXAMPLE

Table starts:

[n] [k=1,2,...] row sum

[1] [1] 1

[2] [1, 3] 4

[3] [2, 3, 7] 12

[4] [4, 6, 7, 19] 36

[5] [9, 12, 14, 19, 46] 100

[6] [20, 27, 28, 38, 46, 129] 288

[7] [48, 60, 63, 76, 92, 129, 337] 805

[8] [115, 144, 140, 171, 184, 258, 337, 939] 2288

[9] [286, 345, 336, 380, 414, 516, 674, 939, 2581] 6471

PROG

(Sage)

@cached_function

def t():

    n = 1

    b = [0, 1]

    while True:

        S = [b[n-k+1]*sum(d*b[d] for d in divisors(k)) for k in (1..n)]

        b.append(sum(S)//n)

        yield S

        n += 1

t_list = t()

for n in (1..12): print(next(t_list))

CROSSREFS

T(n,0) = A000081(n).

T(n,n) = A209397(n).

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

Cf. A275331.

Sequence in context: A084388 A136389 A332057 * A141863 A071010 A215934

Adjacent sequences:  A275327 A275328 A275329 * A275331 A275332 A275333

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 18 2016

STATUS

approved

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Last modified June 5 06:41 EDT 2020. Contains 334828 sequences. (Running on oeis4.)