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 A000751 Boustrophedon transform of partition numbers. 5
 1, 2, 5, 14, 42, 143, 555, 2485, 12649, 72463, 461207, 3229622, 24671899, 204185616, 1819837153, 17378165240, 177012514388, 1915724368181, 21952583954117, 265533531724484, 3380877926676504, 45199008472762756 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS John Cerkan, Table of n, a(n) for n = 0..482 Peter Luschny, An old operation on sequences: the Seidel transform J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (Abstract, pdf, ps). N. J. A. Sloane, Transforms Wikipedia, Boustrophedon_transform FORMULA a(n) = Sum_{k=0..n} A109449(n,k)*A000041(k). - Reinhard Zumkeller, Nov 03 2013 EXAMPLE The array begins:                    1                1  ->   2            5  <-   4  <-   2        3  ->   8  ->  12  ->  14   42  <-  39  <-  31  <-  19  <-   5 - John Cerkan, Jan 26 2017 MATHEMATICA t[n_, 0] := PartitionsP[n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *) PROG (Haskell) a000751 n = sum \$ zipWith (*) (a109449_row n) a000041_list -- Reinhard Zumkeller, Nov 03 2013 (Python) from itertools import accumulate, count, islice from sympy import npartitions def A000751_gen(): # generator of terms     blist = tuple()     for i in count(0):         yield (blist := tuple(accumulate(reversed(blist), initial=npartitions(i))))[-1] A000751_list = list(islice(A000751_gen(), 40)) # Chai Wah Wu, Jun 12 2022 CROSSREFS Cf. A000733, A230957. Sequence in context: A149877 A149878 A148332 * A000744 A047046 A063545 Adjacent sequences:  A000748 A000749 A000750 * A000752 A000753 A000754 KEYWORD nonn,changed AUTHOR STATUS approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)