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A181411 a(n) = Sum_{k=0..n} C(n,k)*sigma(n+k) for n>=1. 1
4, 18, 55, 150, 379, 915, 2146, 4934, 11080, 24833, 54476, 119091, 259432, 556700, 1195135, 2561094, 5428597, 11488866, 24350993, 51296325, 107427025, 225330244, 472762497, 985966379, 2049357779, 4267962522, 8887535983, 18431783744 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..28.

FORMULA

Equals the logarithmic derivative of A181410.

EXAMPLE

L.g.f.: L(x) = 4*x + 18*x^2/2 + 55*x^3/3 + 150*x^4/4 + 379*x^5/5 +...

Exponentiation yields the g.f. of A181410:

exp(L(x)) = 1 + 4*x + 17*x^2 + 65*x^3 + 234*x^4 + 804*x^5 +...

The initial terms begin:

a(1) = 1*1 + 1*3 = 4;

a(2) = 1*3 + 2*4 + 1*7 = 18;

a(3) = 1*4 + 3*7 + 3*6 + 1*12 = 55;

a(4) = 1*7 + 4*6 + 6*12 + 4*8 + 1*15 = 150; ...

PROG

(PARI) {a(n)=sum(k=0, n, binomial(m, k)*sigma(n+k))}

CROSSREFS

Cf. A181410.

Sequence in context: A212250 A229788 A242206 * A238915 A212680 A027286

Adjacent sequences:  A181408 A181409 A181410 * A181412 A181413 A181414

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 19 2010

STATUS

approved

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Last modified July 21 06:28 EDT 2019. Contains 325191 sequences. (Running on oeis4.)