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 A136658 Row sums of unsigned triangle A136656 and also of triangle 2*A136657. 5
 1, 2, 10, 68, 580, 5912, 69784, 933200, 13912336, 228390560, 4088594464, 79186453568, 1648396356160, 36678170613632, 868239454798720, 21776352497954048, 576629116655862016, 16069766602389885440, 470015788927133039104, 14392014594072635786240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..432 FORMULA a(n) = Sum_{k=0..n} (-1)^n*A136656(n,k), n>=0. E.g.f.: exp(x*(2-x)/(1-x)^2) (from Jabotinsky type triangle). a(n) = Sum_{k=0..n} Stirling1(n, k) * Bell(k) * (-1)^(n-k) * 2^k. - Paul D. Hanna, Dec 25 2011 a(n) = (3*n-1)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Sep 25 2013 a(n) ~ 2^(1/6)*n^(n-1/6) * exp((n/2)^(1/3)+3*(n/2)^(2/3)-n-2/3) / sqrt(3) * (1 + 7/(27*(n/2)^(1/3)) - 422/(3645*(n/2)^(2/3))). - Vaclav Kotesovec, Sep 25 2013 Representation as special values of hypergeometric functions 2F2, in Maple notation: a(n) = (n+1)!*hypergeom([(1/2)*n+1, (1/2)*n+3/2], [3/2, 2], 1)*exp(-1), n = 1,2,... . - Karol A. Penson, Jul 28 2018 MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(       binomial(n-1, j-1)*(j+1)!*a(n-j), j=1..n))     end: seq(a(n), n=0..25);  # Alois P. Heinz, Aug 01 2017 MATHEMATICA a[n_] := Sum[ StirlingS1[n, k] * BellB[k] * (-1)^(n-k) * 2^k, {k, 0, n}]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jul 09 2013, after Paul D. Hanna *) Table[Sum[BellY[n, k, (Range[n] + 1)!], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *) PROG (PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)} {Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)} {a(n)=sum(k=0, n, Stirling1(n, k)*Bell(k) * (-1)^(n-k)*2^k)} /* Paul D. Hanna, Dec 25 2011 */ CROSSREFS Cf. A049376, A136656, A136657. Sequence in context: A136633 A082580 A231492 * A329475 A165968 A104098 Adjacent sequences:  A136655 A136656 A136657 * A136659 A136660 A136661 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Feb 22 2008 STATUS approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)