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A234643 E.g.f.: Sum_{n>=0} Integral^n (exp(x) + 1)^n dx^n, where integral^n F(x) dx^n is the n-th integration of F(x) with no constant of integration. 0
1, 2, 5, 13, 35, 99, 297, 951, 3265, 12047, 47761, 202975, 921281, 4447327, 22737537, 122639583, 695404929, 4132531679, 25667031937, 166211936735, 1119791799425, 7833568488415, 56802921911681, 426267651506655, 3305731721387649, 26457699508131807, 218276886237532033 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = Sum_{k=0..n} Sum_{j=0..k} binomial(k,j) * j^(n-k).

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 5*x^2/2! + 13*x^3/3! + 35*x^4/4! + 99*x^5/5! +...

where the e.g.f. may be expressed as a series involving iterated integration:

A(x) = 1 + Integral (exp(x)+1) dx + Integral^2 (exp(x)+1)^2 dx^2 + Integral^3 (exp(x)+1)^3 dx^3 + Integral^4 (exp(x)+1)^4 dx^4 +...

PROG

(PARI) {a(n)=sum(k=0, n, sum(j=0, k, binomial(k, j)*j^(n-k)))}

for(n=0, 30, print1(a(n), ", "))

(PARI) {INTEGRATE(n, F)=local(G=F); for(i=1, n, G=intformal(G)); G}

{a(n)=local(A=1+x); A=1+sum(k=1, n, INTEGRATE(k, (exp(x+x*O(x^n))+1)^k )); n!*polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A105795.

Sequence in context: A126221 A107086 A294790 * A089846 A258450 A131868

Adjacent sequences:  A234640 A234641 A234642 * A234644 A234645 A234646

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 29 2013

STATUS

approved

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Last modified April 26 12:20 EDT 2019. Contains 322472 sequences. (Running on oeis4.)