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A284860 Alternating row sums of the Sheffer triangle (exp(x), exp(3*x) - 1) given in A282629. 2
1, -2, -5, 19, 178, 175, -7739, -72056, -33179, 6899311, 87861076, 215532301, -11151014291, -222077806202, -1563185592617, 22953386817343, 878911293113026, 12330887396253691, 1416506544326449, -4284948239134152536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A282629 for details. This is a generalization of A000587.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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, (DobiƄski type formula).- Wolfdieter Lang, Apr 10 2017

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A282629, A000110, A284859.

Sequence in context: A198203 A014466 A304981 * A108799 A193674 A085871

Adjacent sequences:  A284857 A284858 A284859 * A284861 A284862 A284863

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Apr 05 2017

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)