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A101509 Binomial transform of tau(n) (see A000005). 4
1, 3, 7, 16, 35, 75, 159, 334, 696, 1442, 2976, 6123, 12562, 25706, 52492, 107014, 217877, 443061, 899957, 1826078, 3701783, 7498261, 15178255, 30706320, 62085915, 125465715, 253415981, 511608490, 1032427637, 2082680887, 4199956101, 8467124805, 17064784905, 34382825363, 69256687719, 139465867773 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of A101508.

Also: Number of matrices with positive integer coefficients such that the sum of all entries equals n+1, cf. link "Partitions and A101509". - M. F. Hasler, Jan 14 2009

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..500

L. Manor, M. F. Hasler, Partitions and A101509. SeqFan list, Jan 14 2009

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=0..n, Sum_{i=0..n, if(mod(i+1, k+1)=0, binomial(n, i), 0)}}.

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

MAPLE

bintr:= proc(p) proc(n) add(p(k) *binomial(n, k), k=0..n) end end:

a:= bintr(n-> numtheory[tau](n+1)):

seq(a(n), n=0..40);  # Alois P. Heinz, Jan 30 2011

MATHEMATICA

a[n_] := Sum[DivisorSigma[0, k+1]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Feb 18 2017 *)

PROG

(PARI) A101509(n) = sum( k=0, n, numdiv(k+1)*binomial(n, k)) [M. F. Hasler, Jan 14 2009]

CROSSREFS

Cf. A000005 (tau), A101508, A160399.

Sequence in context: A238913 A133124 A104004 * A240741 A240742 A240743

Adjacent sequences:  A101506 A101507 A101508 * A101510 A101511 A101512

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Dec 05 2004

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.