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A049378 Row sums of triangle A049353. 6
1, 1, 6, 46, 436, 4956, 65776, 996976, 16957536, 319259296, 6581662336, 147290942976, 3552885191296, 91827536814976, 2530228890080256, 74003737259670016, 2288810287491774976, 74607500831801289216, 2555587654482227055616, 91746983502042106018816 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
FORMULA
E.g.f. exp(p(x)) with p(x) := x*(2-x)*(2-2*x+x^2)/(4*(1-x)^4) (E.g.f. first column of A049353).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1)*(j+3)!/4!*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 01 2017
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, j - 1]*(j + 3)!/4!*a[n - j], {j, 1, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *)
CROSSREFS
Cf. A049353.
Sequence in context: A111531 A052781 A284109 * A365056 A218497 A261499
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 01 2017
STATUS
approved

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Last modified April 25 11:24 EDT 2024. Contains 371967 sequences. (Running on oeis4.)