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A050946
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"Stirling-Bernoulli transform" of Fibonacci numbers.
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4
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0, 1, 1, 7, 13, 151, 421, 6847, 25453, 532231, 2473141, 63206287, 352444093, 10645162711, 69251478661, 2413453999327, 17943523153933, 708721089607591, 5927841361456981, 261679010699505967, 2431910546406522973, 118654880542567722871
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| O.g.f.: Sum_{n>=1} fibonacci(n) * n! * x^n / Product_{k=1..n} (1+k*x). [From Paul D. Hanna, Jul 20 2011]
A100872(n)=a(2*n) and A100868(n)=a(2*n-1).
E.g.f.: exp(x)*(1-exp(x))/(1-3*exp(x)+exp((2*x))); a(n)=sum{k=0..n, (-1)^(n-k)*S2(n, k)*Fibonacci(k)}. - Paul Barry, Apr 20 2005
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PROG
| (PARI) {a(n)=polcoeff(sum(m=0, n, fibonacci(m)*m!*x^m/prod(k=1, m, 1+k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */
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CROSSREFS
| Cf. A051782.
Sequence in context: A128351 A192894 A198947 * A178956 A181492 A084963
Adjacent sequences: A050943 A050944 A050945 * A050947 A050948 A050949
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 02 2000
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