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a(n) = (n+1) * A005493(n).
2

%I #13 May 27 2019 17:20:34

%S 1,6,30,148,755,4044,22841,136056,853452,5625950,38885297,281170080,

%T 2122313505,16688829122,136457754030,1158155642512,10186602918035,

%U 92711977180164,871936904575985,8462913158427580,84668764368102012,872196382566014506,9241557859113581689

%N a(n) = (n+1) * A005493(n).

%C A127740 = (n+1) * each term in Aitken's triangle, A011971.

%C A127741 = row sums of A127740.

%H Chai Wah Wu, <a href="/A127741/b127741.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = (n+1) * A005493(n), where A005493 = row sums of Aitken's triangle: (1, 3, 10, 37, ...); i.e., 1*1, 2*3, 3*10, 4*37, ... Row sums of A127740.

%e a(n) = sum of terms in n-th row of A127740. a(2) = 30 = (6 + 9 + 15).

%o (Python)

%o # requires Python 3.2 or higher. Otherwise use def'n of accumulate in Python docs.

%o from itertools import accumulate

%o A127741_list, blist, b = [], [1], 1

%o for n in range(1,1001):

%o ....blist = list(accumulate([b]+blist))

%o ....b = blist[-1]

%o ....A127741_list.append(blist[-2]*n) # _Chai Wah Wu_, Sep 20 2014

%Y Cf. A000110, A052889, A011971, A127740.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Jan 27 2007

%E Edited by _Jon E. Schoenfield_, May 27 2019