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A189238 E.g.f. x/cos(x)*exp(x/cos(x)) 1
1, 2, 6, 28, 120, 726, 4424, 31928, 249984, 2131690, 20027392, 199240020, 2162269824, 24676708798, 302660939520, 3897794538864, 53264941301760, 763279034957010, 11499327153704960, 181271619624350860 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A(x)=A009843(x)*exp(A009843(x)).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

FORMULA

a(n)=sum(k=1..n-1, binomial(n,k)*k*(1+(-1)^(n-k))*sum(j=1..m, sum(i=0..floor((j-1)/2), binomial(m,j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j,i)*(j-2*i)^(n-k)))*binomial(k+m-1,k-1),m,1,n-k))+n.

PROG

(Maxima)

a(n):=sum(binomial(n, k)*k*(1+(-1)^(n-k))*sum(sum(binomial(m, j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j, i)*(j-2*i)^(n-k), i, 0, floor((j-1)/2)), j, 1, m)*binomial(k+m-1, k-1), m, 1, n-k), k, 1, n-1)+n;

(PARI) x='x+O('x^66); /* that many terms */

egf=x/cos(x)*exp(x/cos(x)); /* = x + x^2 + x^3 + 7/6*x^4 + x^5 + 121/120*x^6+ ... */

Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */

CROSSREFS

Sequence in context: A323268 A089748 A047125 * A226497 A307523 A065577

Adjacent sequences:  A189235 A189236 A189237 * A189239 A189240 A189241

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Apr 19 2011

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)