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A191237
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E.g.f. exp(x+x^3+x^5)
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2
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1, 1, 1, 7, 25, 181, 1201, 5251, 57457, 469225, 4340161, 50118751, 412902601, 5544552157, 69259632625, 816044592091, 12518563864801, 152563427413201, 2401979910598657, 39326158638385975, 575414895837696121
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..125
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FORMULA
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a(n)=n!*sum(k=1..n, ((-1)^(n-k)+1)*sum(binomial(j,(n-k)/2-j)*binomial(k,j),j,0,k)/(2*k!)), n>0, a(0)=1.
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MATHEMATICA
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a[n_] := n!*Sum[((-1)^(n - k) + 1)* Sum[ Binomial[j, (n - k)/2 - j]*Binomial[k, j], {j, 0, k}]/(2*k!), {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 21 2013 *)
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PROG
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(Maxima)
a(n):=n!*sum(((-1)^(n-k)+1)*sum(binomial(j, (n-k)/2-j)*binomial(k, j), j, 0, k)/(2*k!), k, 1, n);
(Pari) x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x+x^3+x^5))) /* show terms */ /* Joerg Arndt, May 28 2011 */
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CROSSREFS
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Sequence in context: A082651 A151491 A208425 * A088009 A208823 A197913
Adjacent sequences: A191234 A191235 A191236 * A191238 A191239 A191240
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KEYWORD
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nonn
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AUTHOR
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Vladimir Kruchinin, May 27 2011
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STATUS
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approved
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