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A101510 Diagonal sums of binomial-Möbius product. 3
1, 2, 5, 10, 21, 43, 87, 175, 352, 707, 1417, 2836, 5674, 11353, 22716, 45443, 90886, 181748, 363451, 726870, 1453773, 2907648, 5815315, 11630195, 23259059, 46515887, 93029852, 186060921, 372129424, 744272221, 1488552317, 2977079872 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal sums of A101508.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..floor(n/2)} Sum_{i=0..n-k, (k+1)|(i+1)} binomial(n-k,i).

G.f.: (1/x^2) * Sum_{n>=1} a*z^n/(1-a*z^n) (generalized Lambert series) where z=x/(1-x) and a=x. - Joerg Arndt, Jan 30 2011

a(n) ~ log(2) * 2^(n+1). - Vaclav Kotesovec, Mar 18 2019

MATHEMATICA

a[n_] := Sum[If[Mod[i+1, k+1] == 0, Binomial[n-k, i], 0], {k, 0, n/2}, {i, 0, n-k}]; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Jan 24 2014 *)

nmax = 40; CoefficientList[Series[(1/x^2) * Sum[x*(x/(1-x))^k/(1-x*(x/(1-x))^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 18 2019 *)

PROG

(PARI) a(n) = sum(k=0, n\2, sum(i=0, n-k, if (!Mod(i+1, k+1), binomial(n-k, i)))); \\ Michel Marcus, Mar 16 2019

CROSSREFS

Sequence in context: A027437 A267444 A267880 * A066819 A114279 A101400

Adjacent sequences:  A101507 A101508 A101509 * A101511 A101512 A101513

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Dec 05 2004

STATUS

approved

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Last modified May 26 07:44 EDT 2019. Contains 323579 sequences. (Running on oeis4.)