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A284860
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Alternating row sums of the Sheffer triangle (exp(x), exp(3*x) - 1) given in A282629.
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3
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1, -2, -5, 19, 178, 175, -7739, -72056, -33179, 6899311, 87861076, 215532301, -11151014291, -222077806202, -1563185592617, 22953386817343, 878911293113026, 12330887396253691, 1416506544326449, -4284948239134152536
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OFFSET
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0,2
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COMMENTS
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See A282629 for details. This is a generalization of A000587.
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LINKS
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Table of n, a(n) for n=0..19.
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FORMULA
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a(n) = Sum_{m=0..n} (-1)^m*A282629(n, m), n >= 0.
E.g.f.: exp(x)*exp(1 - exp(3*x)).
a(n) = (1/e)*Sum_{m>=0} ((-1)^m / m!)*(1 + 3*m)^n, n >= 0, (Dobiński type formula).- Wolfdieter Lang, Apr 10 2017
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MATHEMATICA
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Fold[#2 - #1 &, Reverse@ #] & /@ Table[Sum[Binomial[m, k] (-1)^(k - m) (1 + 3 k)^n/m!, {k, 0, m}], {n, 0, 19}, {m, 0, n}] (* Michael De Vlieger, Apr 08 2017 *)
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PROG
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(PARI) T(n, m) = sum(k=0, m, binomial(m, k) * (-1)^(k - m) * (1 + 3*k)^n/m!);
a(n) = sum(m=0, n, (-1)^m*T(n, m)); \\ Indranil Ghosh, Apr 10 2017
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CROSSREFS
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Cf. A282629, A000110, A284859.
Sequence in context: A198203 A014466 A304981 * A108799 A193674 A085871
Adjacent sequences: A284857 A284858 A284859 * A284861 A284862 A284863
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang, Apr 05 2017
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STATUS
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approved
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