

A275330


Triangle read by rows, T(n,k) = t(nk+1)*Sum_{dk} 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
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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[nk+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



