The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356372 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A356372

a(n) = Sum_{k=1..n} binomial(2*n, k) * A000005(k).
(history; published version)

#9 by Hugo Pfoertner at Fri Aug 05 06:18:08 EDT 2022

STATUS

reviewed

approved

#8 by Vaclav Kotesovec at Fri Aug 05 03:03:14 EDT 2022

STATUS

proposed

reviewed

#7 by Michel Marcus at Fri Aug 05 02:35:47 EDT 2022

STATUS

editing

proposed

#6 by Michel Marcus at Fri Aug 05 02:35:44 EDT 2022

PROG

(PARI) a(n) = sum(k=1, n, binomial(2*n, k) * numdiv(k)); \\ Michel Marcus, Aug 05 2022

STATUS

proposed

editing

#5 by Vaclav Kotesovec at Fri Aug 05 01:43:02 EDT 2022

STATUS

editing

proposed

#4 by Vaclav Kotesovec at Thu Aug 04 12:19:02 EDT 2022

FORMULA

a(n) ~ 2^(2*n-1) * (log(n) + 2*gamma), where gamma is the Euler-Mascheroni constant A001620.

#3 by Vaclav Kotesovec at Thu Aug 04 11:58:51 EDT 2022

NAME

allocated for Vaclav Kotesovec

a(n) = Sum_{k=1..n} binomial(2*n, k) * A000005(k).

DATA

2, 16, 76, 386, 1474, 7349, 26807, 121964, 487068, 2105087, 7486505, 37278746, 133488216, 550615531, 2263230587, 9856735046, 35168418266, 160420872009, 573578559659, 2582163925152, 10333237435638, 41122278086361, 146621866522577, 712999981650663, 2702556741014621

OFFSET

1,1

MATHEMATICA

Table[Sum[Binomial[2*n, k]*DivisorSigma[0, k], {k, 1, n}], {n, 1, 30}]

CROSSREFS

Cf. A000005, A006218, A160399, A351146.

KEYWORD

allocated

nonn

AUTHOR

Vaclav Kotesovec, Aug 04 2022

STATUS

approved

editing

#2 by Vaclav Kotesovec at Thu Aug 04 11:57:33 EDT 2022

KEYWORD

allocating

allocated

#1 by Vaclav Kotesovec at Thu Aug 04 11:57:33 EDT 2022

NAME

allocated for Vaclav Kotesovec

KEYWORD

allocating

STATUS

approved