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A009212
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E.g.f. exp(sin(x)*exp(x)).
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0
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1, 1, 3, 9, 33, 137, 619, 3017, 15617, 84625, 474771, 2723721, 15730209, 89487257, 482793211, 2259370697, 6292321025, -41172399839, -1066104760797, -14517156416247, -163539106749663, -1652237279663959, -15169567281615221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=2*sum(k=1..n, sum(j=0..(n-k)/2, binomial(n,n-k-2*j)*(k^(n-k-2*j)*sum(i=0..k/2, (2*i-k)^(k+2*j)*binomial(k,i)*(-1)^(k+j-i))))/(2^k*k!)), n>0, a(0)=1. [From Vladimir Kruchinin, Jun 13 2011]
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MATHEMATICA
| Array[ SeriesCoefficient[ Series[ Exp[ Sin[ x ]*Exp[ x ] ], {x, 0, 30} ], # ]*#!&, 29, 0 ]
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PROG
| (Maxima)
a(n):=2*sum(sum(binomial(n, n-k-2*j)*(k^(n-k-2*j)*sum((2*i-k)^(k+2*j)*binomial(k, i)*(-1)^(k+j-i), i, 0, k/2)), j, 0, (n-k)/2)/(2^k*k!), k, 1, n); [From Vladimir Kruchinin, Jun 13 2011]
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CROSSREFS
| Sequence in context: A151043 A151044 A098742 * A153344 A193110 A001930
Adjacent sequences: A009209 A009210 A009211 * A009213 A009214 A009215
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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