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A344501 a(n) = Sum_{k=0..n} binomial(n, k)*HT(n, k) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*HT(n, k), where HT(n, k) is the Hermite triangle A099174. 1
1, 1, 2, 10, 40, 176, 916, 4852, 27350, 163270, 1009396, 6504356, 43400512, 298682320, 2118282440, 15433768456, 115345136566, 882900083222, 6910879999420, 55255039432300, 450744068706896, 3747796352076736, 31734090674951512, 273414453918459800, 2395202886317347900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n) = Sum_{j=0..n} even(n - j)*binomial(n, j)*2^((j - n)/2)*n!/(j!*((n - j)/2)!), where even(k) = 1 if k is even and otherwise 0.

MAPLE

a := proc(n) add((if n - j mod 2 = 0 then binomial(n, j)*2^((j - n)/2)*n!/(j!*((n - j)/2)!) else 0 fi), j = 0..n) end: seq(a(n), n = 0..24);

CROSSREFS

Cf. A099174, A344500.

Sequence in context: A223095 A052978 A151023 * A151024 A151025 A333799

Adjacent sequences:  A344498 A344499 A344500 * A344502 A344503 A344504

KEYWORD

nonn

AUTHOR

Peter Luschny, May 22 2021

STATUS

approved

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Last modified October 17 12:01 EDT 2021. Contains 348048 sequences. (Running on oeis4.)